Recent zbMATH articles in MSC 93B https://zbmath.org/atom/cc/93B 2023-09-22T14:21:46.120933Z Werkzeug Weak identifiability for differential algebraic systems https://zbmath.org/1517.12006 2023-09-22T14:21:46.120933Z "Jeronimo, Gabriela" https://zbmath.org/authors/?q=ai:jeronimo.gabriela "Solernó, Pablo" https://zbmath.org/authors/?q=ai:solerno.pablo Summary: We introduce a new notion of parameter identifiability for ODE systems following a multi-experiment approach. We show that a system that is identifiable according to previous well-known notions is also identifiable with our definition, but that the converse is not always true. In this sense, we speak of \textit{weak identifiability}. We provide finite criteria to check weak identifiability and present algorithms that decide whether a system is weakly identifiable or not. The transfer matrix of differential-algebraic equations https://zbmath.org/1517.34012 2023-09-22T14:21:46.120933Z "Shcheglova, A. A." https://zbmath.org/authors/?q=ai:shcheglova.alla-arkadevna This paper is devoted to the study of the transfer function of linear differential-algebraic equations. The author considers the system \begin{aligned} A\frac{d}{dt} x(t) + Bx(t)+ Uu(t)=&0,\quad t\in T=[0,\infty) \\ y(t)=Cx&(t), \end{aligned}\tag{1} with some known real $$n \times n$$ matrices $$A$$ and $$B$$, such that $$\mathrm{det} A = 0$$, an unknown $$n$$-dimensional vector function $$x(t)$$, a known $$n \times l$$ matrix $$U$$, a known $$m \times n$$ matrix $$C$$, an $$l$$-dimensional vector control function $$u(t)$$, and an $$m$$-dimensional output $$y(t)$$. The transfer function of system (1) is defined by $\mathcal H(s)=-C(sA+B)^{-1}U\tag{2}$ which characterizes the input-output relation. The author proposes a construction of a minimal realization of the transfer matrix in the class of DAEs of index 1 with separated differential and algebraic subsystems. It is shown that such a realization is minimal if and only if it is controllable and observable. Note that the problem of constructing a minimal realization of the transfer matrix for DAEs has already been addressed by several other authors. However, the author's method is claimed to be simpler. The author also discusses the stability of the transfer function (2). Finally, the author considers the transfer matrix of a system of DAEs depending on an uncertain parameter and proposes an algorithm for constructing a minimal realization of the matrix polynomial as an algebraic subsystem. Reviewer: Vu Hoang Linh (Hà Nội) Qualitative behavior of a metabolic pathway with hybrid feedback https://zbmath.org/1517.34069 2023-09-22T14:21:46.120933Z "Lopez-Zazueta, Claudia" https://zbmath.org/authors/?q=ai:lopez-zazueta.claudia "Fromion, Vincent" https://zbmath.org/authors/?q=ai:fromion.vincent Summary: We study the qualitative behavior of a model to represent local regulation in a metabolic network. The model is based on the end-product control structure introduced in [\textit{A. Goelzer} et al., BMC Syst. Biol. 2, No. 1, Article ID 20, 18 p. (2008; \url{doi:10.1186/1752-0509-2-20})]. In this class of regulation, the metabolite effector is the end product of a metabolic pathway. We suppose the input to the pathway to switch between zero and a positive value according to the concentration of the metabolite effector. Considering the switching system as a differential inclusion, we prove that it converges to a globally uniformly asymptotically stable equilibrium point, reaches the sliding mode, or oscillates around the sliding mode depending on the positive value of the input. Finally, we show that in any case the solution of the switching system is the limit of solutions of equation sequences with smooth or piecewise linear inputs. The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension https://zbmath.org/1517.34081 2023-09-22T14:21:46.120933Z "Kuznetsov, N. V." https://zbmath.org/authors/?q=ai:kuznetsov.nikolay-v "Mokaev, T. N." https://zbmath.org/authors/?q=ai:mokaev.timur-nazirovich "Kuznetsova, O. A." https://zbmath.org/authors/?q=ai:kuznetsova.olga-aleksandrovna "Kudryashova, E. V." https://zbmath.org/authors/?q=ai:kudryashova.elena-vladimirovna (no abstract) Chaos transition of the generalized fractional Duffing oscillator with a generalized time delayed position feedback https://zbmath.org/1517.34087 2023-09-22T14:21:46.120933Z "El-Borhamy, Mohamed" https://zbmath.org/authors/?q=ai:el-borhamy.mohamed (no abstract) Approximate controllability of semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control https://zbmath.org/1517.34109 2023-09-22T14:21:46.120933Z "Annamalai, Anguraj" https://zbmath.org/authors/?q=ai:annamalai.anguraj "Kasinathan, Ravikumar" https://zbmath.org/authors/?q=ai:kasinathan.ravikumar "Kasinathan, Ramkumar" https://zbmath.org/authors/?q=ai:kasinathan.ramkumar Summary: The objective of this paper is to interpret the approximate controllability of a semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control in infinite-dimensional spaces. Sufficient conditions for the approximate controllability of semi-linear control system have been established. The results are obtained using the Banach fixed point theorem and the theory of resolvent operator developed in [\textit{R. C. Grimmer}, Trans. Am. Math. Soc. 273, 333--349 (1982; Zbl 0493.45015)]. An example is introduced to show the effectiveness of the result. Boundary controllability and stabilizability of a coupled first-order hyperbolic-elliptic system https://zbmath.org/1517.35098 2023-09-22T14:21:46.120933Z "Chowdhury, Shirshendu" https://zbmath.org/authors/?q=ai:chowdhury.shirshendu "Dutta, Rajib" https://zbmath.org/authors/?q=ai:dutta.rajib "Majumdar, Subrata" https://zbmath.org/authors/?q=ai:majumdar.subrata Summary: In this paper, we study the controllability of a coupled first-order hyperbolic-elliptic system in the interval $$(0,1)$$ by a Dirichlet boundary control acting at the left endpoint of the hyperbolic component only. Using the multiplier approach and compactness-uniqueness argument, we establish the exact controllability for the hyperbolic component of the model, at any time $$T>1$$. We explore the method of moments to conclude the exact controllability at the critical time $$T=1$$. For the case of small time, that is for $$T<1$$, we show that the system is not null controllable. Further, using a Gramian-based approach introduced by Urquiza, we prove the exponential stabilization of the corresponding closed-loop system with arbitrary prescribed decay rate by means of boundary feedback control law. Exact controllability of semilinear heat equations through a constructive approach https://zbmath.org/1517.35125 2023-09-22T14:21:46.120933Z "Ervedoza, Sylvain" https://zbmath.org/authors/?q=ai:ervedoza.sylvain "Lemoine, Jérôme" https://zbmath.org/authors/?q=ai:lemoine.jerome "Münch, Arnaud" https://zbmath.org/authors/?q=ai:munch.arnaud Summary: The exact distributed controllability of the semilinear heat equation $$\partial_ty-\Delta y+f(y)=v1_\omega$$ posed over multi-dimensional and bounded domains, assuming that $$f$$ is locally Lipschitz continuous and satisfies the growth condition $$\limsup_{|r|\to\infty}|f(r)|/(|r|\ln^{3/2}|r|)\le\beta$$ for some $$\beta$$ small enough has been obtained by \textit{E. Fernández-Cara} and \textit{E. Zuazua} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 17, No. 5, 583--616 (2000; Zbl 0970.93023)]. The proof based on a non constructive fixed point arguments makes use of precise estimates of the observability constant for a linearized heat equation. Under the same assumption, by introducing a different fixed point application, we present a different and somewhat simpler proof of the exact controllability, which is not based on the cost of observability of the heat equation with respect to potentials. Then, assuming that $$f$$ is locally Lipschitz continuous and satisfies the growth condition $$\limsup_{|r|\to\infty}|f^\prime(r)|/\ln^{3/2}|r|\le\beta$$ for some $$\beta$$ small enough, we show that the above fixed point application is contracting yielding a constructive method to compute the controls for the semilinear equation. Numerical experiments illustrate the results. Constructive exact control of semilinear 1D heat equations https://zbmath.org/1517.35126 2023-09-22T14:21:46.120933Z "Lemoine, Jérôme" https://zbmath.org/authors/?q=ai:lemoine.jerome "Münch, Arnaud" https://zbmath.org/authors/?q=ai:munch.arnaud Summary: The exact distributed controllability of the semilinear heat equation $$\partial_ty-\Delta y+g(y)=f1_{\omega}$$ posed over multi-dimensional and bounded domains, assuming that $$g\in C^1(\mathbb{R})$$ satisfies the growth condition $$\limsup_{r\to\infty}g(r)/(|r|\ln^{3/2}|r|)=0$$ has been obtained by Fernández-Cara and Zuazua in 2000. The proof based on a non constructive fixed point arguments makes use of precise estimates of the observability constant for a linearized heat equation. In the one dimensional setting, assuming that $$g'$$ does not grow faster than $$\beta\ln^{3/2}|r|$$ at infinity for $$\beta>0$$ small enough and that $$g'$$ is uniformly Hölder continuous on $$\mathbb{R}$$ with exponent $$p\in[0,1]$$, we design a constructive proof yielding an explicit sequence converging to a controlled solution for the semilinear equation, at least with order $$1+p$$ after a finite number of iterations. Analysis and numerical solvability of backward-forward conservation laws https://zbmath.org/1517.35137 2023-09-22T14:21:46.120933Z "Liard, Thibault" https://zbmath.org/authors/?q=ai:liard.thibault "Zuazua, Enrique" https://zbmath.org/authors/?q=ai:zuazua.enrique Summary: In this paper, we study the problem of initial data identification for weak-entropy solutions of the one-dimensional Burgers equation. This problem consists in identifying the set of initial data evolving to a given target at a final time. Due to the time-irreversibility of the Burgers equation, some target functions are unattainable from solutions of this equation, making the identification problem under consideration ill-posed. To get around this issue, we introduce a nonsmooth optimization problem, which consists in minimizing the difference between the predictions of the Burgers equation and the observations of the system at a final time in $$L^2(\mathbb{R})$$ norm. Here, we characterize the set of minimizers of the aforementioned nonsmooth optimization problem. One of the minimizers is the backward entropy solution, constructed using a backward-forward method. Some simulations are given using a wave-front tracking algorithm. Existence of controls insensitizing the rotational of the solution of the Navier-Stokes system having a vanishing component https://zbmath.org/1517.35149 2023-09-22T14:21:46.120933Z "Carreño, N." https://zbmath.org/authors/?q=ai:carreno.nicolas "Prada, J." https://zbmath.org/authors/?q=ai:prada.julia|prada.juan-carlos-garcia Summary: In this paper we study an insensitizing control problem for the Navier-Stokes system. The novelty is that we insensitize the rotational of the solution using controls with one component fixed at zero. This problem can be formulated as a null controllability problem for a nonlinear cascade system for which we follow the usual duality approach. First, we prove a suitable Carleman inequality for a system coupling two Stokes like equations, which leads to the null controllability at any positive time. Finally, we deduce a local null controllability result for the cascade system by a local inverse argument. Desensitizing control for the heat equation with respect to domain variations https://zbmath.org/1517.35232 2023-09-22T14:21:46.120933Z "Ervedoza, Sylvain" https://zbmath.org/authors/?q=ai:ervedoza.sylvain "Lissy, Pierre" https://zbmath.org/authors/?q=ai:lissy.pierre "Privat, Yannick" https://zbmath.org/authors/?q=ai:privat.yannick Summary: This article is dedicated to desensitizing issues for a quadratic functional involving the solution of the linear heat equation with respect to domain variations. This work can be seen as a continuation of [\textit{P. Lissy} et al., ESAIM, Control Optim. Calc. Var. 25, Paper No. 50, 21 p. (2019; Zbl 1442.93009)], insofar as we generalize several of the results it contains and investigate new related properties. In our framework, we consider variations of the spatial domain on which the solution of the PDE is defined at each time, and investigate three main issues: (i) approximate desensitizing, (ii) approximate desensitizing combined with an exact desensitizing for a finite-dimensional subspace, and (iii) exact desensitizing. We provide positive answers to questions (i) and (ii) and partial results to question (iii). Exact and optimal controllability for scalar conservation laws with discontinuous flux https://zbmath.org/1517.35233 2023-09-22T14:21:46.120933Z "Adimurthi" https://zbmath.org/authors/?q=ai:adimurthi.a "Ghoshal, Shyam Sundar" https://zbmath.org/authors/?q=ai:ghoshal.shyam-sundar Summary: This paper describes the reachable set and resolves an optimal control problem for the scalar conservation laws with discontinuous flux. We give a necessary and sufficient criteria for the reachable set. A new backward resolution has been described to obtain the reachable set. Regarding the optimal control problem, we first prove the existence of a minimizer and then the backward algorithm allows us to compute it. The same method also applies to compute the initial data control for an exact control problem. Our methodology for the proof relies on the explicit formula for the conservation laws with the discontinuous flux and finer properties of the characteristics curves. Impulse null approximate controllability for heat equation with dynamic boundary conditions https://zbmath.org/1517.35253 2023-09-22T14:21:46.120933Z "Chorfi, Salah-Eddine" https://zbmath.org/authors/?q=ai:chorfi.salah-eddine "El Guermai, Ghita" https://zbmath.org/authors/?q=ai:el-guermai.ghita "Maniar, Lahcen" https://zbmath.org/authors/?q=ai:maniar.lahcen "Zouhair, Walid" https://zbmath.org/authors/?q=ai:zouhair.walid Summary: The main purpose of this article is to prove a logarithmic convexity estimate for the solution of a linear heat equation subject to dynamic boundary conditions in a bounded convex domain. As an application, we prove the impulsive null approximate controllability for an impulsive heat equation with dynamic boundary conditions. Multifidelity robust controller design with gradient sampling https://zbmath.org/1517.37093 2023-09-22T14:21:46.120933Z "Werner, Steffen W. R." https://zbmath.org/authors/?q=ai:werner.steffen-w-r "Overton, Michael L." https://zbmath.org/authors/?q=ai:overton.michael-l "Peherstorfer, Benjamin" https://zbmath.org/authors/?q=ai:peherstorfer.benjamin Summary: Robust controllers that stabilize dynamical systems even under disturbances and noise are often formulated as solutions of nonsmooth, nonconvex optimization problems. While methods such as gradient sampling can handle the nonconvexity and nonsmoothness, the costs of evaluating the objective function may be substantial, making robust control challenging for dynamical systems with high-dimensional state spaces. In this work, we introduce multifidelity variants of gradient sampling that leverage low-cost, low-fidelity models with low-dimensional state spaces for speeding up the optimization process while nonetheless providing convergence guarantees for a high-fidelity model of the system of interest, which is primarily accessed in the last phase of the optimization process. Our first multifidelity method initiates gradient sampling on higher-fidelity models with starting points obtained from cheaper, lower-fidelity models. Our second multifidelity method relies on ensembles of gradients that are computed from low- and high-fidelity models. Numerical experiments with controlling the cooling of a steel rail profile and laminar flow in a cylinder wake demonstrate that our new multifidelity gradient sampling methods achieve up to two orders of magnitude speedup compared to the single-fidelity gradient sampling method that relies on the high-fidelity model alone. HJB-RBF based approach for the control of PDEs https://zbmath.org/1517.49016 2023-09-22T14:21:46.120933Z "Alla, Alessandro" https://zbmath.org/authors/?q=ai:alla.alessandro "Oliveira, Hugo" https://zbmath.org/authors/?q=ai:oliveira.hugo-luiz "Santin, Gabriele" https://zbmath.org/authors/?q=ai:santin.gabriele Summary: Semi-Lagrangian schemes for the discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems due to the curse of dimensionality. Here, we present a new approach for infinite horizon optimal control problems where the value function is computed using radial basis functions by the Shepard moving least squares approximation method on scattered grids. We propose a new method to generate a scattered mesh driven by the dynamics and the selection of the shape parameter in the RBF using an optimization routine. This mesh will help to localize the problem and approximate the dynamic programming principle in high dimension. Error estimates for the value function are also provided. Numerical tests for high dimensional problems will show the effectiveness of the proposed method. A note on a very recent paper Feedback control for nonlinear evolutionary equations with applications'' https://zbmath.org/1517.49021 2023-09-22T14:21:46.120933Z "Yin, Bin" https://zbmath.org/authors/?q=ai:yin.bin "Zeng, Biao" https://zbmath.org/authors/?q=ai:zeng.biao In this paper, the authors correct and improve the proofs of the main lemmas in a very recent publication [\textit{B. Zeng}, Nonlinear Anal., Real World Appl. 66, Article ID 103535, 21 p. (2022; Zbl 1481.49008)], in which the hypotheses of boundedness, coerciveness and relaxed monotonicity for the operators are considered. Reviewer: Savin Treanţă (Bucureşti) Controllability of neutral stochastic functional integro-differential equations driven by fractional Brownian motion with Hurst parameter lesser than $$1/2$$ https://zbmath.org/1517.60059 2023-09-22T14:21:46.120933Z "Boufoussi, Brahim" https://zbmath.org/authors/?q=ai:boufoussi.brahim "Mouchtabih, Soufiane" https://zbmath.org/authors/?q=ai:mouchtabih.soufiane Summary: This article investigates the controllability for neutral stochastic delay functional integro-differential equations driven by a fractional Brownian motion, with Hurst parameter lesser than $$1/2$$. We employ the theory of resolvent operators developed by \textit{R. C. Grimmer} [Trans. Am. Math. Soc. 273, 333--349 (1982; Zbl 0493.45015)] combined with the Banach fixed point theorem to establish sufficient conditions to prove the desired result. Robust controller synthesis for duration calculus https://zbmath.org/1517.68230 2023-09-22T14:21:46.120933Z "Dole, Kalyani" https://zbmath.org/authors/?q=ai:dole.kalyani "Gupta, Ashutosh" https://zbmath.org/authors/?q=ai:gupta.ashutosh "Krishna, Shankara Narayanan" https://zbmath.org/authors/?q=ai:krishna.shankara-narayanan Summary: In automatic control synthesis, we may need to handle specifications with timing constraints and control such that the system meets the specification as much as possible, which is called robust control. In this paper, we present a method for open loop robust controller synthesis from duration calculus (DC) specifications. For robust synthesis, we propose an approach to evaluate the robustness of DC specifications on a given run of a system. We leverage a CEGIS like method for synthesizing robust control signals. In our method, the DC specifications and the system under control are encoded into mixed integer linear problems, and the optimization problem is solved to yield a control signal. We have implemented a tool (ControlDC) based on the method and applied it on a set of benchmarks. For the entire collection see [Zbl 1502.68030]. Analysis of dynamical behaviors of a 2-DOF friction oscillator with elastic impacts and negative feedbacks https://zbmath.org/1517.70024 2023-09-22T14:21:46.120933Z "Gao, Min" https://zbmath.org/authors/?q=ai:gao.min "Fan, Jinjun" https://zbmath.org/authors/?q=ai:fan.jinjun (no abstract) Invariant spectral foliations with applications to model order reduction and synthesis https://zbmath.org/1517.70039 2023-09-22T14:21:46.120933Z "Szalai, Robert" https://zbmath.org/authors/?q=ai:szalai.robert (no abstract) Quantitative analysis on the phase margin of ADRC https://zbmath.org/1517.70046 2023-09-22T14:21:46.120933Z "Zhong, Sheng" https://zbmath.org/authors/?q=ai:zhong.sheng "Huang, Yi" https://zbmath.org/authors/?q=ai:huang.yi.9 (no abstract) Using nonlinear feedback control to improve aircraft nose landing gear shimmy performance https://zbmath.org/1517.74069 2023-09-22T14:21:46.120933Z "Wang, Yong" https://zbmath.org/authors/?q=ai:wang.yong.3|wang.yong.25|wang.yong.11|wang.yong.16|wang.yong.6|wang.yong.1|wang.yong|wang.yong.8|wang.yong.5|wang.yong.15|wang.yong.27|wang.yong.29|wang.yong.10|wang.yong.7|wang.yong.17|wang.yong.14|wang.yong.2|wang.yong.18|wang.yong.13 "Jin, Xianyu" https://zbmath.org/authors/?q=ai:jin.xianyu "Yin, Yin" https://zbmath.org/authors/?q=ai:yin.yin Summary: Shimmy vibration is a common oscillation in the nose landing gear (NLG) during aircraft landing and taxiing process, which is a potentially dangerous phenomenon. Herein, the nonlinear angular velocity feedback (NAVF) control is proposed to enhance the shimmy performance of the NLG. The five-dimensional dynamic model of the NLG with NAVF control is established based on the rotational and lateral dynamic model, as well as the stretched string tire model. The numerical continuation and bifurcation analysis methods are used to study the shimmy performance of the NLG, the stable region and limit cycle oscillation (LCO) amplitude are obtained. The effect of square and cubic NAVF gain on the stable region and LCO amplitude are compared, as well as the resonance frequency amplitude of rotational and lateral motion. Furthermore, the suppression effect of higher-order NAVF control on the shimmy performance of the NLG is discussed. The results show that the NAVF control can enlarge the stable region and decrease the LCO amplitude of the NLG. A larger feedback gain is beneficial to reduce the rotational angle and narrow the rotational shimmy region. The square NAVF control can shrink the rotational shimmy region. The cubic and higher-order NAVF control can significantly reduce the LCO amplitude of the rotational shimmy. Therefore, the NAVF control can improve the shimmy performance of the NLG and provide an effective option for designing NLG in practical engineering. Local predictability and coherence versus distributed entanglement in entanglement swapping from partially entangled pure states https://zbmath.org/1517.81022 2023-09-22T14:21:46.120933Z "Maziero, Jonas" https://zbmath.org/authors/?q=ai:maziero.jonas "Basso, Marcos L. W." https://zbmath.org/authors/?q=ai:basso.marcos-l-w "Céleri, Lucas C." https://zbmath.org/authors/?q=ai:celeri.lucas-c Summary: Complete complementarity relations, as e.g. $$P(\rho_A)^2 + C(\rho_A)^2 + E(|\Psi\rangle_{AB})^2 = 1$$, constrain the local predictability and local coherence and the entanglement of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in [\textit{M. L. W. Basso} and \textit{J. Maziero}, Phys. Lett., A 451, Article ID 128414, 5 p. (2022; Zbl 1511.81023)] to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-basis measurement of the entanglement swapping protocol (ESP). In this article, we extend this result for general pure initial states. We obtain a general relation between pre-measurement local predictability and coherence and the distributed entanglement in the ESP. We use IBM's quantum computers to verify experimentally some instances of these general theoretical results. Frequency domain techniques for $$H_\infty$$ control of distributed parameter systems https://zbmath.org/1517.93001 2023-09-22T14:21:46.120933Z "Özbay, Hitay" https://zbmath.org/authors/?q=ai:ozbay.hitay "Gümüşsoy, Suat" https://zbmath.org/authors/?q=ai:gumussoy.suat "Kashima, Kenji" https://zbmath.org/authors/?q=ai:kashima.kenji "Yamamoto, Yutaka" https://zbmath.org/authors/?q=ai:yamamoto.yutaka The book is a comprehensive and pedagogical introduction to $$\mathcal{H} _{\infty }$$-control of infinite-dimensional linear systems. It contains new results compared to the book [\textit{C. Foias} et al., Robust control of infinite dimensional systems. Frequency domain methods. Berlin: Springer-Verlag (1996; Zbl 0839.93003)]. Like this one, the book under review focuses on frequency-domain techniques. The latter are illustrated by many examples for which a MATLAB program is provided. This is of course very attractive and useful for the student or the practicing engineer. The greatest part of the book (Chapters 1 to 6) deals with SISO systems whereas MIMO systems are considered in Chapter 7. The book contains a rich bibliography (284 references) and an Index. Several types of infinite-dimensional systems are considered: delay systems (of retarded or neutral type) and systems with a pseudorational transfer function. The reader familiar with $$\mathcal{H}_{\infty }$$-control of finite-dimensional systems should not have too great difficulties to read this book and use it. The type of stability considered is $$\mathcal{H}_{\infty }$$-stability, i.e. a linear system is called stable if and only if its transfer function belongs to the Hardy space $$\mathcal{H}_{\infty }$$. This point of view is very reasonable in the case of finite-dimensional systems since, assuming that such a systems is controllable and observable, it is asymptotically stable if and only if its transfer function belongs to $$\mathcal{H}_{\infty }$$. The case of infinite-dimensional systems is quite different since, in general, the state of such a system is not defined. An exception is when the system evolution is characterized by a semigroup of operators as in [\textit{R. F. Curtain} and \textit{H. Zwart}, An introduction to infinite-dimensional linear systems theory. New York, NY: Springer-Verlag (1995; Zbl 0839.93001)]; see also [\textit{H. Bourlès}, Théorie des systèmes -- une approche moderne 1. London: ISTE Editions (2022)] in the case of linear delay systems of retarded or neutral type. Reviewer: Henri Bourlès (Paris) Linear multivariable control systems https://zbmath.org/1517.93002 2023-09-22T14:21:46.120933Z "Bhattacharyya, Shankar P." https://zbmath.org/authors/?q=ai:bhattacharyya.shankar-prashad "Keel, Lee H." https://zbmath.org/authors/?q=ai:keel.lee-h Publisher's description: This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering. Output-constrained control of non-affine multi-agent systems with actuator faults and unknown dead zones https://zbmath.org/1517.93005 2023-09-22T14:21:46.120933Z "Li, Shubo" https://zbmath.org/authors/?q=ai:li.shubo.1 "Pan, Yingnan" https://zbmath.org/authors/?q=ai:pan.yingnan "Liang, Hongjing" https://zbmath.org/authors/?q=ai:liang.hongjing Summary: This paper presents the output-constrained control algorithm for non-affine multi-agent systems (MASs) with actuator faults and unknown dead zones. The error transformation method is employed to keep initial connectivity patterns in the non-affine MASs for consensus tracking control. The radial basis function neural networks are utilized to estimate the unknown nonlinear functions. Furthermore, the Nussbaum function is used to overcome partially unknown control direction problem. To address the problem of the constrained control, a state transformation technique is presented. In addition, the fault-tolerant consensus tracking protocol is designed to reduce the effects of actuator faults and dead zones. Furthermore, it is shown that the consensus tracking errors are cooperatively semi-globally uniformly ultimately bounded. Finally, the effectiveness of the proposed approach is illustrated by some simulation results. Autonomous and non-autonomous fixed-time leader-follower consensus for second-order multi-agent systems https://zbmath.org/1517.93007 2023-09-22T14:21:46.120933Z "Trujillo, M. A." https://zbmath.org/authors/?q=ai:trujillo.miguel-a "Aldana-López, R." https://zbmath.org/authors/?q=ai:aldana-lopez.rodrigo "Gómez-Gutiérrez, D." https://zbmath.org/authors/?q=ai:gomez-gutierrez.david "Defoort, M." https://zbmath.org/authors/?q=ai:defoort.michael "Ruiz-León, J." https://zbmath.org/authors/?q=ai:ruiz-leon.javier "Becerra, H. M." https://zbmath.org/authors/?q=ai:becerra.hector-m (no abstract) Consensus tracking via quantized iterative learning control for singular nonlinear multi-agent systems with state time-delay and initial state error https://zbmath.org/1517.93009 2023-09-22T14:21:46.120933Z "Zhou, Xingyu" https://zbmath.org/authors/?q=ai:zhou.xingyu "Wang, Haoping" https://zbmath.org/authors/?q=ai:wang.haoping "Tian, Yang" https://zbmath.org/authors/?q=ai:tian.yang "Dai, Xisheng" https://zbmath.org/authors/?q=ai:dai.xisheng (no abstract) Controlling, optimizing, deciding https://zbmath.org/1517.93010 2023-09-22T14:21:46.120933Z "Franck, Emmanuel" https://zbmath.org/authors/?q=ai:franck.emmanuel "Privat, Yannick" https://zbmath.org/authors/?q=ai:privat.yannick This paper is a short survey of three domains related to automation: control/controllability, optimal control, and planning/decision. The paper is nicely written (in French) and is intended for both the expert in usual control methods who will be happy to realize that (and how) his/her area of expertise is a part of a wider domain, including learning methods, and to the expert in applied mathematics, familiar with various learning methods, and for whom an introduction to control theory is necessary. The paper is of course too short to be a comprehensive introduction. The two basic notions of controllability (exact and approximate controllability) are briefly reviewed. The optimal control is then considered. J. L. Lions's HUM method is mentioned as well as its connection to controllability. The two usual methods for continuous-time systems (Pontryagin's maximum principle and the Hamilton-Jacobi-Bellman approach) are not mentioned. Nevertheless, Bellman's dynamic programming is considered in the last section on planning/decision. Various refinements of this approach are mentioned, such as Q-learning. Reviewer: Henri Bourlès (Paris) Null boundary controllability for some biological and chemical diffusion problems https://zbmath.org/1517.93011 2023-09-22T14:21:46.120933Z "Ismailov, Mansur I." https://zbmath.org/authors/?q=ai:ismailov.mansur-i "Oner, Isil" https://zbmath.org/authors/?q=ai:oner.isil Summary: We examine the null boundary controllability of diffusion problems (with non-local boundary conditions) arising from the morphogen concentration process and the electrochemistry. Two different types of semi-periodic conditions are addressed. Also, towards further applications to biological and chemical diffusion problems, we comment on anti-semi-periodic boundary conditions. Such boundary conditions make the auxiliary spectral problems non-self-adjoint and, therefore the classical eigenfunctions expansion method does not work. The systems of eigenfunctions form a Riesz basis in the $$L_2$$ space by adding associated eigenfunctions. For the controllability, we determine the admissible classes of initial data in terms of their Fourier coefficients. Finally, we present the null boundary controllability of these problems by the reduction to the moment problem. Controllability of suspension bridge model proposed by Lazer and McKenna under the influence of impulses, delays, and non-local conditions https://zbmath.org/1517.93012 2023-09-22T14:21:46.120933Z "Zouhair, Walid" https://zbmath.org/authors/?q=ai:zouhair.walid "Leiva, Hugo" https://zbmath.org/authors/?q=ai:leiva.hugo Summary: The main purpose of this paper is to prove the controllability of the model proposed by Lazer and Mckenna under the influence of impulses, delay, and non-local conditions. First, we study approximate controllability by employing a technique that pulls back the control solution to a fixed curve in a short time interval. Subsequently, based on Banach Fixed Point Theorem we investigate the exact controllability. $$\varepsilon$$-embedding model reduction method for time-delay differential algebra systems https://zbmath.org/1517.93013 2023-09-22T14:21:46.120933Z "Qiu, Zhi-Yong" https://zbmath.org/authors/?q=ai:qiu.zhiyong "Jiang, Yao-Lin" https://zbmath.org/authors/?q=ai:jiang.yaolin Summary: A new model order reduction (MOR) method for large-scale time-delay differential algebra systems is proposed herein. The presented MOR algorithm is based on parametric moment matching and $$\varepsilon$$-embedding. By selecting an appropriate projection matrix, this process generates reduced-order models that preserve the structure of the original time-delay differential algebra system. Additionally, moment-matching results and error estimations are provided. Finally, two numerical circuits are tested to illustrate the effectiveness of the proposed MOR method. Predefined-time control of distributed-order systems https://zbmath.org/1517.93014 2023-09-22T14:21:46.120933Z "Muñoz-Vázquez, Aldo Jonathan" https://zbmath.org/authors/?q=ai:munoz-vazquez.aldo-jonathan "Fernández-Anaya, Guillermo" https://zbmath.org/authors/?q=ai:fernandez-anaya.guillermo "Sánchez-Torres, Juan Diego" https://zbmath.org/authors/?q=ai:sanchez-torres.juan-diego "Meléndez-Vázquez, Fidel" https://zbmath.org/authors/?q=ai:melendez-vazquez.fidel (no abstract) A geometric algebra approach to invariance control in sliding regimes for switched systems https://zbmath.org/1517.93015 2023-09-22T14:21:46.120933Z "Sira-Ramírez, H." https://zbmath.org/authors/?q=ai:sira-ramirez.hebertt-j "Gómez-León, B. C." https://zbmath.org/authors/?q=ai:gomez-leon.brian-c "Aguilar-Orduña, M. A." https://zbmath.org/authors/?q=ai:aguilar-orduna.mario-andres Sliding mode control systems, affine in the binary-valued control law, are considered. Known results are presented by using in a systematic way a geometric algebra framework, as follows: necessary and sufficient conditions for the existence of a sliding regime, a characterization of the equivalent control, and the invariance control approach. Within this framework it is shown that the twisting and super twisting algorithms may be obtained as a limiting case of first order regimes. Examples are discussed in detail. Reviewer: Tullio Zolezzi (Genova) Implementation of integral fixed-time sliding mode controller for speed regulation of PMSM servo system https://zbmath.org/1517.93016 2023-09-22T14:21:46.120933Z "Wang, Linan" https://zbmath.org/authors/?q=ai:wang.linan "Du, Haibo" https://zbmath.org/authors/?q=ai:du.haibo "Zhang, Weijian" https://zbmath.org/authors/?q=ai:zhang.weijian.1 "Wu, Di" https://zbmath.org/authors/?q=ai:wu.di "Zhu, Wenwu" https://zbmath.org/authors/?q=ai:zhu.wenwu (no abstract) Fixed-time SOSM controller design with output constraint https://zbmath.org/1517.93017 2023-09-22T14:21:46.120933Z "Yuan, Jiahao" https://zbmath.org/authors/?q=ai:yuan.jiahao "Ding, Shihong" https://zbmath.org/authors/?q=ai:ding.shihong "Mei, Keqi" https://zbmath.org/authors/?q=ai:mei.keqi (no abstract) High-order sliding mode observer-based trajectory tracking control for a quadrotor UAV with uncertain dynamics https://zbmath.org/1517.93018 2023-09-22T14:21:46.120933Z "Zhao, Zhenhua" https://zbmath.org/authors/?q=ai:zhao.zhenhua "Cao, Dong" https://zbmath.org/authors/?q=ai:cao.dong "Yang, Jun" https://zbmath.org/authors/?q=ai:yang.jun.5 "Wang, Huiming" https://zbmath.org/authors/?q=ai:wang.huiming (no abstract) Recursive identification of errors-in-variables systems based on the correlation analysis https://zbmath.org/1517.93019 2023-09-22T14:21:46.120933Z "Fan, Shujun" https://zbmath.org/authors/?q=ai:fan.shujun "Ding, Feng" https://zbmath.org/authors/?q=ai:ding.feng "Hayat, Tasawar" https://zbmath.org/authors/?q=ai:hayat.tasawar Summary: This paper considers a single-input single-output linear dynamic system, whose input and output are corrupted by Gaussian white measurement noises with zero means and unknown variances; the parameter estimation of such a system is a typical errors-in-variables (EIV) system identification problem. This paper proposes the correlation function-based two-step identification methods for the EIV systems. In order to obtain the unbiased parameter estimates of the EIV system, we derive the correlation function equation by using the correlation analysis method and adopt the least squares method and the instrumental variable method to recursively compute the parameter estimates of the model, resulting in the unbiased parameter estimates of the EIV systems. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms. Identification and nonlinearity compensation of hysteresis using NARX models https://zbmath.org/1517.93020 2023-09-22T14:21:46.120933Z "Abreu, Petrus E. O. G. B." https://zbmath.org/authors/?q=ai:abreu.petrus-e-o-g-b "Tavares, Lucas A." https://zbmath.org/authors/?q=ai:tavares.lucas-a "Teixeira, Bruno O. S." https://zbmath.org/authors/?q=ai:teixeira.bruno-otavio-soares "Aguirre, Luis A." https://zbmath.org/authors/?q=ai:aguirre.luis-antonio (no abstract) Bayesian system ID: optimal management of parameter, model, and measurement uncertainty https://zbmath.org/1517.93021 2023-09-22T14:21:46.120933Z "Galioto, Nicholas" https://zbmath.org/authors/?q=ai:galioto.nicholas "Gorodetsky, Alex Arkady" https://zbmath.org/authors/?q=ai:gorodetsky.alex-arkady (no abstract) Command filtered robust control of nonlinear systems with full-state time-varying constraints and disturbances rejection https://zbmath.org/1517.93022 2023-09-22T14:21:46.120933Z "Yang, Guichao" https://zbmath.org/authors/?q=ai:yang.guichao "Wang, Hua" https://zbmath.org/authors/?q=ai:wang.hua.2|wang.hua.4|wang.hua.5|wang.hua.6|wang.hua.1|wang.hua "Chen, Jie" https://zbmath.org/authors/?q=ai:chen.jie.9|chen.jie.1|chen.jie.2|chen.jie.5|chen.jie.3|chen.jie.10|chen.jie.11|chen.jie.6|chen.jie.13|chen.jie "Zhang, Hao" https://zbmath.org/authors/?q=ai:zhang.hao-helen|zhang.hao.3|zhang.hao|zhang.hao.5|zhang.hao.9|zhang.hao.4|zhang.hao.2 (no abstract) Exploring robustness management for dynamic technology fusion https://zbmath.org/1517.93023 2023-09-22T14:21:46.120933Z "Zhu, Jianhua" https://zbmath.org/authors/?q=ai:zhu.jianhua "Liu, Wanchun" https://zbmath.org/authors/?q=ai:liu.wanchun "Li, Yonghui" https://zbmath.org/authors/?q=ai:li.yonghui "Sun, Yanming" https://zbmath.org/authors/?q=ai:sun.yanming (no abstract) A delay-dependent approach to finite-time $$H_\infty$$ control of nonlinear descriptor systems with state delay via observer-based control https://zbmath.org/1517.93024 2023-09-22T14:21:46.120933Z "Binazadeh, Tahereh" https://zbmath.org/authors/?q=ai:binazadeh.tahereh "Asadinia, Maryam Sadat" https://zbmath.org/authors/?q=ai:asadinia.maryam-sadat Summary: This paper proposes a finite-time observer-based controller for time-delay descriptor systems with time-varying disturbances, model uncertainties, and one-sided Lipschitz nonlinearities. For this purpose, first, a nonlinear descriptor observer is designed, and the observer error system is calculated. Then, the observer-based control law is proposed to provide the conditions for robust stabilization of the closed-loop descriptor system by selecting an appropriate Lyapunov-Krasovskii functional. According to the delay-dependent stability criterion, LMI-based sufficient conditions are derived and the gains of the controller and the observer are calculated. The proposed controller guarantees the finite-time boundedness and $$H_\infty$$ disturbance attenuation of the closed-loop descriptor system. Finally, the effectiveness of the proposed technique is investigated through computer simulations. Event-triggering $$H_\infty$$-based observer combined with NN for simultaneous estimation of vehicle sideslip and roll angles with network-induced delays https://zbmath.org/1517.93025 2023-09-22T14:21:46.120933Z "Boada, Maria Jesus L." https://zbmath.org/authors/?q=ai:boada.maria-jesus-l "Boada, Beatriz L." https://zbmath.org/authors/?q=ai:boada.beatriz-l "Zhang, Hui" https://zbmath.org/authors/?q=ai:zhang.hui.3|zhang.hui.20|zhang.hui|zhang.hui.12|zhang.hui.17|zhang.hui.5|zhang.hui.4|zhang.hui.6|zhang.hui.15|zhang.hui.25|zhang.hui.2|zhang.hui.13|zhang.hui.11|zhang.hui.14|zhang.hui.8|zhang.hui.9|zhang.hui.21 (no abstract) Adaptive event-triggered $$H_{\infty }$$ control for Markov jump systems with generally uncertain transition rates https://zbmath.org/1517.93026 2023-09-22T14:21:46.120933Z "Chen, Lin" https://zbmath.org/authors/?q=ai:chen.lin.2|chen.lin.1|chen.lin|chen.lin.11|chen.lin.5 "Li, Xiaomeng" https://zbmath.org/authors/?q=ai:li.xiaomeng "Lin, Wenshuai" https://zbmath.org/authors/?q=ai:lin.wenshuai "Zhou, Qi" https://zbmath.org/authors/?q=ai:zhou.qi.2 Summary: This paper considers the adaptive event-triggered $$H_{\infty }$$ control issue for Markov jump systems with generally uncertain transition rates and actuator faults. Compared with the conventional method, an adaptive event-triggered mechanism with a varying threshold is adopted to save the communication resources effectively. The general model of transition rates in Markov jump process includes completely unknown and uncertain bounded as two special models. Based on linear matrix inequalities, the sufficient conditions of the controller design can be obtained to guarantee the closed-loop systems are stochastically stable. Finally, simulation examples are exploited to verify the effectiveness of the proposed control strategy. Data-driven gradient-based point-to-point iterative learning control for nonlinear systems https://zbmath.org/1517.93027 2023-09-22T14:21:46.120933Z "Huo, Benyan" https://zbmath.org/authors/?q=ai:huo.benyan "Freeman, Chris T." https://zbmath.org/authors/?q=ai:freeman.chris-t "Liu, Yanghong" https://zbmath.org/authors/?q=ai:liu.yanghong (no abstract) Dynamical distributed control and synchronization https://zbmath.org/1517.93028 2023-09-22T14:21:46.120933Z "Flores-Flores, Juan Pablo" https://zbmath.org/authors/?q=ai:flores-flores.juan-pablo "Martínez-Guerra, Rafael" https://zbmath.org/authors/?q=ai:martinez-guerra.rafael (no abstract) Controller design for switched systems with non-symmetrical input saturation https://zbmath.org/1517.93029 2023-09-22T14:21:46.120933Z "Wang, Qian" https://zbmath.org/authors/?q=ai:wang.qian.10 "Wu, Zhengguang" https://zbmath.org/authors/?q=ai:wu.zhengguang "Chen, Yun" https://zbmath.org/authors/?q=ai:chen.yun Summary: In this paper, a state feedback controller is designed for switched systems with non-symmetrical input saturation based on two classes of parametric Riccati equation (PRE). Through appropriate mathematical transformation, we transform a switched system with non-symmetrical input saturation to a switched system with multiple equilibrium points and symmetrical input saturation. The exponential stability of the switched system is investigated using the good properties of PRE. The main contributions of this paper include (a) solving the non-symmetrical input saturation control problem for the switched system; (b) designing a controller to guarantee the exponential stability of the switched system with the subsystems having the open-loop critical stable poles; (c) the designed controller can be easily computed by solving the PRE. The controller is easy to implement in practical applications. A numerical example is provided to illustrate the effectiveness and potential of the proposed method. Controller design for fractional-order interconnected systems with unmodeled dynamics https://zbmath.org/1517.93030 2023-09-22T14:21:46.120933Z "Hua, Changchun" https://zbmath.org/authors/?q=ai:hua.changchun "Ning, Jinghua" https://zbmath.org/authors/?q=ai:ning.jinghua "Guan, Xinping" https://zbmath.org/authors/?q=ai:guan.xinping (no abstract) Output feedback regulation of large-scale feedforward systems with discrete and distributed delays https://zbmath.org/1517.93031 2023-09-22T14:21:46.120933Z "Liu, Qingrong" https://zbmath.org/authors/?q=ai:liu.qingrong "Li, Hanfeng" https://zbmath.org/authors/?q=ai:li.hanfeng "Zhu, Fei" https://zbmath.org/authors/?q=ai:zhu.fei "Zhang, Xianfu" https://zbmath.org/authors/?q=ai:zhang.xianfu (no abstract) A homogeneous domination output feedback control method for active suspension of intelligent electric vehicle https://zbmath.org/1517.93032 2023-09-22T14:21:46.120933Z "Meng, Qinghua" https://zbmath.org/authors/?q=ai:meng.qinghua "Qian, Chunjiang" https://zbmath.org/authors/?q=ai:qian.chunjiang "Sun, Zong-Yao" https://zbmath.org/authors/?q=ai:sun.zongyao "Chen, Chih-Chiang" https://zbmath.org/authors/?q=ai:chen.chih-chiang (no abstract) Finite-time non-fragile boundary feedback control for a class of nonlinear parabolic systems https://zbmath.org/1517.93033 2023-09-22T14:21:46.120933Z "Wei, Chengzhou" https://zbmath.org/authors/?q=ai:wei.chengzhou "Li, Junmin" https://zbmath.org/authors/?q=ai:li.junmin (no abstract) Multi-objective frequency domain-constrained static output feedback control for delayed active suspension systems with wheelbase preview information https://zbmath.org/1517.93034 2023-09-22T14:21:46.120933Z "Zhao, Jing" https://zbmath.org/authors/?q=ai:zhao.jing.4 "Wang, Xiaowei" https://zbmath.org/authors/?q=ai:wang.xiaowei.1|wang.xiaowei "Wong, Pak Kin" https://zbmath.org/authors/?q=ai:wong.pak-kin "Xie, Zhengchao" https://zbmath.org/authors/?q=ai:xie.zhengchao "Jia, Junru" https://zbmath.org/authors/?q=ai:jia.junru "Li, Wenfeng" https://zbmath.org/authors/?q=ai:li.wenfeng (no abstract) Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation https://zbmath.org/1517.93035 2023-09-22T14:21:46.120933Z "Zhou, Xin" https://zbmath.org/authors/?q=ai:zhou.xin.7 "Gao, Chuang" https://zbmath.org/authors/?q=ai:gao.chuang "Li, Zhi-gang" https://zbmath.org/authors/?q=ai:li.zhigang "Ouyang, Xin-yu" https://zbmath.org/authors/?q=ai:ouyang.xinyu "Wu, Li-bing" https://zbmath.org/authors/?q=ai:wu.libing (no abstract) Finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays https://zbmath.org/1517.93036 2023-09-22T14:21:46.120933Z "Aouiti, Chaouki" https://zbmath.org/authors/?q=ai:aouiti.chaouki "Bessifi, Mayssa" https://zbmath.org/authors/?q=ai:bessifi.mayssa "Li, Xiaodi" https://zbmath.org/authors/?q=ai:li.xiaodi Summary: This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get subsystems with real values covered by the framework of differential inclusions, and novel time-delays feedback controllers are constructed to understand the synchronization problem in finite time and fixed time of error system. Second, by creating Lyapunov functions and applying some differential inequalities, several new criteria are derived to get the synchronization in finite time and fixed time of the studied neural networks. Finally, two numerical examples are presented to justify the effectiveness of our results. Fluctuation response patterns of network dynamics -- an introduction https://zbmath.org/1517.93037 2023-09-22T14:21:46.120933Z "Zhang, Xiaozhu" https://zbmath.org/authors/?q=ai:zhang.xiaozhu "Timme, Marc" https://zbmath.org/authors/?q=ai:timme.marc Summary: Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to pandemics spreading across continents. Most of such systems are driven by irregular and distributed fluctuating input signals from the environment. Yet how networked dynamical systems collectively respond to such fluctuations depends on the location and type of driving signal, the interaction topology and several other factors and remains largely unknown to date. As a key example, modern electric power grids are undergoing a rapid and systematic transformation towards more sustainable systems, signified by high penetrations of renewable energy sources. These in turn introduce significant fluctuations in power input and thereby pose immediate challenges to the stable operation of power grid systems. How power grid systems dynamically respond to fluctuating power feed-in as well as other temporal changes is critical for ensuring a reliable operation of power grids yet not well understood. In this work, we systematically introduce a linear response theory (LRT) for fluctuation-driven networked dynamical systems. The derivations presented not only provide approximate analytical descriptions of the dynamical responses of networks, but more importantly, also allow to extract key qualitative features about spatio-temporally distributed response patterns. Specifically, we provide a general formulation of a LRT for perturbed networked dynamical systems, explicate how dynamic network response patterns arise from the solution of the linearised response dynamics, and emphasise the role of LRT in predicting and comprehending power grid responses on different temporal and spatial scales and to various types of disturbances. Understanding such patterns from a general, mathematical perspective enables to estimate network responses quickly and intuitively, and to develop guiding principles for, e.g., power grid operation, control and design. Nonlinear model reduction for wave energy systems: a moment-matching-based approach https://zbmath.org/1517.93038 2023-09-22T14:21:46.120933Z "Faedo, Nicolás" https://zbmath.org/authors/?q=ai:faedo.nicolas "Dores Piuma, Francisco Javier" https://zbmath.org/authors/?q=ai:dores-piuma.francisco-javier "Giorgi, Giuseppe" https://zbmath.org/authors/?q=ai:giorgi.giuseppe "Ringwood, John V." https://zbmath.org/authors/?q=ai:ringwood.john-v (no abstract) Adaptive prescribed performance control for nonlinear pure-feedback systems: a scalarly virtual parameter adaptation approach https://zbmath.org/1517.93044 2023-09-22T14:21:46.120933Z "Wu, Chen" https://zbmath.org/authors/?q=ai:wu.chen "Gao, Shigen" https://zbmath.org/authors/?q=ai:gao.shigen "Dong, Hairong" https://zbmath.org/authors/?q=ai:dong.hairong (no abstract) Sliding mode control and its application in switched systems: a survey https://zbmath.org/1517.93048 2023-09-22T14:21:46.120933Z "Liu, Qi" https://zbmath.org/authors/?q=ai:liu.qi "Jiang, Baoping" https://zbmath.org/authors/?q=ai:jiang.baoping "Wu, Zhengtian" https://zbmath.org/authors/?q=ai:wu.zhengtian "Chen, Zhengping" https://zbmath.org/authors/?q=ai:chen.zhengping "Hao, Wanjun" https://zbmath.org/authors/?q=ai:hao.wanjun Summary: According to the development and research of sliding mode variable structure control (SMVSC) in recent years. This paper mainly reviews the development and applications of some popular sliding mode control (SMC), such as adaptive SMC, discrete-time system SMC, fuzzy SMC, and neural network SMC. With the research and development of switched system (SS), the research scholars can deal with the complex and changeable system more effectively by combining the SMC with the SS, so as to improve the efficiency and stability of the system. The theoretical research and applications of SMC combined with fuzzy SS, predictive SS and uncertainty SS are also becoming more and more attractive. The purpose of this paper is to analyze and organize the current research status of the popular directions of SMC, and provide the readers with the latest research results on the application directions and new trends in the field of SMC. By considering these theoretical studies and numerous applications, the research and development of intelligent control techniques and switching systems based on sliding mode control are reviewed. Finally, some prospects for related research are presented. Robust time-varying tracking control of sandwich nonlinear systems with sandwiched saturation nonlinearity https://zbmath.org/1517.93049 2023-09-22T14:21:46.120933Z "Azhdari, Meysam" https://zbmath.org/authors/?q=ai:azhdari.meysam "Binazadeh, Tahereh" https://zbmath.org/authors/?q=ai:binazadeh.tahereh Summary: This paper addresses the output-tracking control problem for a class of nonlinear sandwich systems with external disturbances and model uncertainties. Sandwich systems are a special class of nonlinear systems in the cascade structure, which are made up of several distinct subsystems while the non-smooth nonlinear functions are sandwiched among their separate subsystems. This paper concentrates on the sandwich systems consisting of two arbitrary-order nonlinear cascaded subsystems, while the saturation nonlinearity is sandwiched between them. The robust control law is designed such that the output of the sandwich system tracks the desired time-varying reference signal despite the saturation occurrence. Due to the characteristics of the saturation function and also the existence of the external disturbances and model uncertainties, the considered problem is facing some serious challenges. To deal with these difficulties, the design procedure is divided into two phases. In the first phase, the second subsystem and the sandwiched saturation nonlinearity are considered. In this phase, by utilizing the backstepping approach, the desired input signal of the saturation function is designed. In the second phase, the control input of the first subsystem is designed based on the sliding mode technique in a way that the output of the first subsystem tracks the desired signal which is obtained in the first phase. Finally, to verify the effectiveness of the proposed method, it is applied to a practical sandwich system. Adaptive type-2 neural fuzzy sliding mode control of a class of nonlinear systems https://zbmath.org/1517.93051 2023-09-22T14:21:46.120933Z "Khan, Muhammad Umair" https://zbmath.org/authors/?q=ai:khan.muhammad-umair "Kara, Tolgay" https://zbmath.org/authors/?q=ai:kara.tolgay (no abstract) On the algorithmic stability of optimal control with derivative operators https://zbmath.org/1517.93053 2023-09-22T14:21:46.120933Z "Chen, Tim" https://zbmath.org/authors/?q=ai:chen.tim "Cheng, J. C.-Y." https://zbmath.org/authors/?q=ai:cheng.j-c-y Summary: The aim of this paper is to develop a productive numerical technique to deal with a class of time partial ideal AI control issues. The classical fuzzy inference methods cannot work to their full potential in such circumstances, because the given knowledge does not cover the entire problem domain. In addition, the requirements of fuzzy systems may change over time. The use of a static rule base may affect the effectiveness of fuzzy rule interpolation due to the absence of the most concurrent (dynamic) rules. The experimental result indicates that evolved bat algorithm with our proposed fitness function presents a 93.77\% success rate in average for finding the feasible solutions. The contribution of this study is that near outcomes likewise confirm that the partial administrator for a Mittag-Leffler circuit in the Caputo sense improves the execution of the AI controlled framework as far as the transient reaction, in contrast with the other fragmentary and whole number subordinate administrators. Adaptive fuzzy output-feedback tracking control for switched nonstrict-feedback nonlinear systems with prescribed performance https://zbmath.org/1517.93054 2023-09-22T14:21:46.120933Z "Wang, Yuanqing" https://zbmath.org/authors/?q=ai:wang.yuanqing "Chang, Yi" https://zbmath.org/authors/?q=ai:chang.yi "Alkhateeb, Abdulhameed F." https://zbmath.org/authors/?q=ai:alkhateeb.abdulhameed-f "Alotaibi, Naif D." https://zbmath.org/authors/?q=ai:alotaibi.naif-d Summary: In this article, an adaptive fuzzy output-feedback tracking control scheme is proposed for a class of single-input and single-output uncertain switched nonlinear systems in nonstrict-feedback form with prescribed performance and arbitrary switching. By using the concept of prescribed performance, we mean that the tracking error converges to the predefined performance bounds. The unknown nonlinear functions are approximated by utilizing the fuzzy logic systems. For the systems under study, unavailable states are taken into account, which are estimated by constructing a fuzzy state observer. In order to overcome the difficulty arising from the nonstrict-feedback form, an effective adaptive parameter is introduced. By using the common Lyapunov function method and backstepping design approach, an adaptive control algorithm is presented for the considered system. The designed controller can guarantee that all the signals within closed-loop systems are semi-globally uniformly ultimately bounded. The effectiveness of the control strategy put forward in this paper is demonstrated by the simulation results. Security control of interval type-2 fuzzy system with two-terminal deception attacks under premise mismatch https://zbmath.org/1517.93056 2023-09-22T14:21:46.120933Z "Zhao, Tao" https://zbmath.org/authors/?q=ai:zhao.tao.1 "Zhang, Kunpeng" https://zbmath.org/authors/?q=ai:zhang.kunpeng "Dian, Songyi" https://zbmath.org/authors/?q=ai:dian.songyi (no abstract) Pinning synchronization control for a class of dynamical networks with coupled time-varying delays: an interval-observer-based approach https://zbmath.org/1517.93058 2023-09-22T14:21:46.120933Z "Liu, Linlin" https://zbmath.org/authors/?q=ai:liu.linlin "Wei, Guoliang" https://zbmath.org/authors/?q=ai:wei.guoliang "Wang, Licheng" https://zbmath.org/authors/?q=ai:wang.licheng Summary: This paper is concerned with the pinning synchronization control issue for a class of discrete-time complex dynamical networks. By resorting to the interval observer approach, a novel pinning synchronization control strategy is adopted to control a small fraction of the network nodes with hope to reduce the implementation cost. By using the Lyapunov stability theorem, some synchronization criteria have been derived to ensure the desired synchronization performance. Finally, a numerical simulation is presented to illustrate the effectiveness and usefulness of the theoretical results. Matrix approach for verification of opacity of partially observed discrete event systems https://zbmath.org/1517.93059 2023-09-22T14:21:46.120933Z "Mei, Liujuan" https://zbmath.org/authors/?q=ai:mei.liujuan "Liu, Rongjian" https://zbmath.org/authors/?q=ai:liu.rongjian "Lu, Jianquan" https://zbmath.org/authors/?q=ai:lu.jianquan "Qiu, Jianlong" https://zbmath.org/authors/?q=ai:qiu.jianlong Summary: Opacity is a confidential property characterizing whether the secret of a system can be inferred or not by an outside observer (also called an intruder). This paper focuses on presenting a matrix-based approach for verification of opacity of nondeterministic discrete event systems (DESs). Firstly, the given system is modeled as a finite-state automaton. Further, based on Boolean semi-tensor product (BSTP) of matrices, the algebraic expression of the observable dynamic of the system can be obtained. We, respectively, investigate current-state opacity and $$K$$-step opacity owing to the equivalence between a few opacity properties. Finally, necessary and sufficient conditions are presented to verify whether the secret is opaque for a given system, and the proposed methodology is tested effectively by examples. The matrix-based characterization of opacity proposed in this paper may provide a helpful angel for understanding the structure of this property. Input-and-measurement event-triggered control for flexible air-breathing hypersonic vehicles with asymmetric partial-state constraints https://zbmath.org/1517.93060 2023-09-22T14:21:46.120933Z "Shao, Xingling" https://zbmath.org/authors/?q=ai:shao.xingling "Shi, Yi" https://zbmath.org/authors/?q=ai:shi.yi "Zhang, Wendong" https://zbmath.org/authors/?q=ai:zhang.wen-dong (no abstract) Velocity-sensorless proportional-derivative trajectory tracking control with active damping for quadcopters https://zbmath.org/1517.93062 2023-09-22T14:21:46.120933Z "Kim, Seok-Kyoon" https://zbmath.org/authors/?q=ai:kim.seok-kyoon "Ahn, Choon Ki" https://zbmath.org/authors/?q=ai:ahn.choon-ki (no abstract) Design and experimental validation of a nonlinear controller for underactuated surface vessels https://zbmath.org/1517.93063 2023-09-22T14:21:46.120933Z "Xie, Wei" https://zbmath.org/authors/?q=ai:xie.wei "Reis, Joel" https://zbmath.org/authors/?q=ai:reis.joel "Cabecinhas, David" https://zbmath.org/authors/?q=ai:cabecinhas.david "Silvestre, Carlos" https://zbmath.org/authors/?q=ai:silvestre.carlos-j (no abstract) Disturbance observer-based autonomous landing control of unmanned helicopters on moving shipboard https://zbmath.org/1517.93064 2023-09-22T14:21:46.120933Z "Yu, Xin" https://zbmath.org/authors/?q=ai:yu.xin.2|yu.xin|yu.xin.1 "Yang, Jun" https://zbmath.org/authors/?q=ai:yang.jun.1|yang.jun.12|yang.jun.11|yang.jun.5|yang.jun.10|yang.jun.7|yang.jun.14|yang.jun.9|yang.jun.2 "Li, Shihua" https://zbmath.org/authors/?q=ai:li.shihua.1|li.shihua (no abstract) String stability and flow stability for nonlinear vehicular platoons with actuator faults based on an improved quadratic spacing policy https://zbmath.org/1517.93068 2023-09-22T14:21:46.120933Z "Hao, Li-Ying" https://zbmath.org/authors/?q=ai:hao.liying "Li, Ping" https://zbmath.org/authors/?q=ai:li.ping.4|li.ping|li.ping.1|li.ping.16|li.ping.24|li.ping.5|li.ping.2|li.ping.7|li.ping.8|li.ping.10 "Guo, Ge" https://zbmath.org/authors/?q=ai:guo.ge (no abstract) New results on stability for a class of fractional-order static neural networks https://zbmath.org/1517.93069 2023-09-22T14:21:46.120933Z "Yao, Xiangqian" https://zbmath.org/authors/?q=ai:yao.xiangqian "Tang, Meilan" https://zbmath.org/authors/?q=ai:tang.meilan "Wang, Fengxian" https://zbmath.org/authors/?q=ai:wang.fengxian "Ye, Zhijian" https://zbmath.org/authors/?q=ai:ye.zhijian "Liu, Xinge" https://zbmath.org/authors/?q=ai:liu.xinge Summary: This paper investigates the stability of a class of fractional-order static neural networks. Two new Lyapunov functions with proper integral terms are constructed. These integrals with variable upper limit are convex functions. Based on the fractional-order Lyapunov direct method and some inequality skills, several novel stability sufficient conditions which ensure the global Mittag-Leffler stability of fractional-order projection neural networks (FPNNs) are presented in the forms of linear matrix inequalities (LMIs). Two LMI-based Mittag-Leffler stability criteria with less conservativeness are given for a special kind of FPNNs. Finally, the effectiveness of the proposed method is demonstrated via four numerical examples. Robust finite-time tracking for a square fully actuated class of nonlinear systems https://zbmath.org/1517.93070 2023-09-22T14:21:46.120933Z "Bafghi, Hamidreza Fakharizade" https://zbmath.org/authors/?q=ai:bafghi.hamidreza-fakharizade "Jahed-Motlagh, Mohammad Reza" https://zbmath.org/authors/?q=ai:jahed-motlagh.mohammad-reza "Abooee, Ali" https://zbmath.org/authors/?q=ai:abooee.ali "Moarefianpur, Ali" https://zbmath.org/authors/?q=ai:moarefianpur.ali (no abstract) Robust resource allocation strategy for technology innovation ecosystems: state and control constraints https://zbmath.org/1517.93071 2023-09-22T14:21:46.120933Z "Chen, Xiuqian" https://zbmath.org/authors/?q=ai:chen.xiuqian "Sun, Qinqin" https://zbmath.org/authors/?q=ai:sun.qinqin "Xia, Fei" https://zbmath.org/authors/?q=ai:xia.fei "Chen, Ye-Hwa" https://zbmath.org/authors/?q=ai:chen.ye-hwa (no abstract) On the $$\mu$$-analysis and synthesis of MIMO Lurie-type systems with application in complex networks https://zbmath.org/1517.93072 2023-09-22T14:21:46.120933Z "Fernandes Pinheiro, Rafael" https://zbmath.org/authors/?q=ai:fernandes-pinheiro.rafael "Colón, Diego" https://zbmath.org/authors/?q=ai:colon.diego Summary: The main contribution of this paper is to present a new approach to the analysis of the absolute stability of multiple-input-multiple-output (MIMO) Lurie-type systems using $$\mu$$-analysis and linear fractional transformations from the robust control theory. As a consequence, and also as an important contribution, the technique proposed enables the design of controllers via DK-Iteration for Lurie-type systems. For these, one extends the results obtained for Lurie-type systems to a closed-loop version of it. In addition, it is also conjectured that it is possible to make use of this new approach in time-delay MIMO Lurie-type systems. The obtained results allow a generalization of the theory for the analysis and design of controllers that can be useful in complex networks. Examples and comparisons with other results are given to illustrate the effectiveness of the methods of this paper. Dual-mode global stabilization of high-order saturated integrator chains: LMI-based MPC combined with a nested saturated feedback https://zbmath.org/1517.93073 2023-09-22T14:21:46.120933Z "Adelipour, Saeed" https://zbmath.org/authors/?q=ai:adelipour.saeed "Ahi, Behzad" https://zbmath.org/authors/?q=ai:ahi.behzad "Haeri, Mohammad" https://zbmath.org/authors/?q=ai:haeri.mohammad (no abstract) Asymptotic stabilisation of coupled delayed time fractional reaction diffusion systems with boundary input disturbances via backstepping sliding-mode control https://zbmath.org/1517.93076 2023-09-22T14:21:46.120933Z "Chen, Juan" https://zbmath.org/authors/?q=ai:chen.juan "Zhuang, Bo" https://zbmath.org/authors/?q=ai:zhuang.bo "Yu, Yajuan" https://zbmath.org/authors/?q=ai:yu.yajuan The paper studies asymptotic stabilization of a class of coupled fractional reaction-diffusion systems with time-varying delays and input disturbances of the form $_0^C D_t^\alpha U(x,t) = A(x) U_{xx}(x,t) + \Psi_1 U(x,t-\tau(t)) + \Psi(x) U(x,t)$ $U_x(0,t) - P U(0,t) = 0$ $U_x(1,t) + Q U(1,t) = V_c(t) + \Phi(t)$ $U(x,t) = I(x,t), \quad 0\leq x \leq 1, \quad -h \leq t \leq 0,$ where $$x\in(0,1)$$, $$A(x) = \mathtt{diag}(a_1(x), \ldots, a_n(x))\in\mathbb R^{n\times n}$$, $$n>1$$, $$a_i(x)$$ denote the uniformly bounded space-dependent diffusion coefficient, $$U(x,t) \in \mathbb R^n$$ stands for the state, $$V_c(t), \Phi(t) \in \mathbb R^n$$ represent control inputs and uncertain sufficiently smooth disturbances, respectively. For this purpose of asymptotic stabilization of the considered system, the backstepping-based boundary sliding mode controller is designed. The controller is built upon an invertible backstapping transformation that transforms the original systems into a target dynamics with newly defined inputs and perturbations. Then, the sliding mode algorithm is employed for the design of discontinuous controller that suppresses disturbances. Numerical examples are used to validate the proposed theoretical approach. Reviewer: Petro Feketa (Kiel) Dissipative control of 2-d switched discrete system via dwell-time-dependent approach https://zbmath.org/1517.93077 2023-09-22T14:21:46.120933Z "Hua, Dingli" https://zbmath.org/authors/?q=ai:hua.dingli "Wang, Weiqun" https://zbmath.org/authors/?q=ai:wang.weiqun "Yu, Weiren" https://zbmath.org/authors/?q=ai:yu.weiren "Yao, Juan" https://zbmath.org/authors/?q=ai:yao.juan Summary: This paper studies the dissipative control problem for two-dimensional (2-D) switched discrete-time linear system represented by Fornasini-Marchesini local state-space (FMLSS) model via dwell-time-dependent Lyapunov function (DTDLF) approach. Consider the definition of $$(Q, S, R)$$-$$\alpha$$-dissipativity for 2-D switched discrete FMLSS model in triangular region and based on the DTDLF approach, we first give the linear matrix inequality (LMI)-based sufficient condition on asymptotic stability for the 2-D switched discrete FMLSS model and then propose the LMI-based sufficient condition which can guarantee the given 2-D switched system to be asymptotically stable and strictly $$(Q, S, R)$$-$$\alpha$$-dissipative. Furthermore, the dwell-time-dependent dissipative state-feedback controller is designed, and the LMI-based sufficient condition for designing such controller is proposed. Besides, dwell-time-dependent passive state-feedback controller and dwell-time-dependent $$H_\infty$$ state-feedback controller could be derived as the special cases of dissipative control from the established result. Finally, illustrative examples are depicted to verify the efficiency and superiority of the proposed techniques. Robust fault accommodation strategy of the reentry vehicle: a disturbance estimate-triggered approach https://zbmath.org/1517.93079 2023-09-22T14:21:46.120933Z "Chang, Jing" https://zbmath.org/authors/?q=ai:chang.jing "Guo, Zongyi" https://zbmath.org/authors/?q=ai:guo.zongyi "Cieslak, Jérôme" https://zbmath.org/authors/?q=ai:cieslak.jerome "Henry, David" https://zbmath.org/authors/?q=ai:henry.david.2 (no abstract) Adaptive robust maneuvering control for nonlinear systems via dynamic surface technique https://zbmath.org/1517.93081 2023-09-22T14:21:46.120933Z "Yang, Cun" https://zbmath.org/authors/?q=ai:yang.cun "Wu, Zhaojing" https://zbmath.org/authors/?q=ai:wu.zhaojing (no abstract) Robust adaptive finite-time attitude tracking control of a 3D pendulum with external disturbance: numerical simulations and hardware experiments https://zbmath.org/1517.93082 2023-09-22T14:21:46.120933Z "Yao, Qijia" https://zbmath.org/authors/?q=ai:yao.qijia (no abstract) An optimization framework for the design of noise shaping loop filters with improved stability properties https://zbmath.org/1517.94027 2023-09-22T14:21:46.120933Z "Hannigan, Brett C." https://zbmath.org/authors/?q=ai:hannigan.brett-c "Petersen, Christian L." https://zbmath.org/authors/?q=ai:petersen.christian-l "Mallinson, A. Martin" https://zbmath.org/authors/?q=ai:mallinson.a-martin "Dumont, Guy A." https://zbmath.org/authors/?q=ai:dumont.guy-a Summary: A framework using semidefinite programming is proposed to enable the design of sigma delta modulator loop filters at the transfer function level. Both continuous-time and discrete-time, low-pass and band-pass designs are supported. For performance, we use the recently popularized Generalized Kalman-Yakubovič-Popov (GKYP) lemma to place constraints on the $$\mathcal{H}_\infty$$ norm of the noise transfer function (NTF) in the frequency band of interest. We expand the approach to incorporate common stability criteria in the form of $$\mathcal{H}_2$$ and $$\ell_1$$ norm NTF constraints. Furthering the discussion of stability, we introduce techniques from control systems to improve the robustness of the feedback system over a range of quantizer gains. The performance-stability trade-off is examined using this framework and motivated by simulation results.