Edit Profile (opens in new tab) Grüne, Lars Co-Author Distance Author ID: grune.lars Published as: Grüne, Lars; Grüne, L.; Gruene, Lars more...less Homepage: https://num.math.uni-bayreuth.de/de/team/lars-gruene/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp Documents Indexed: 155 Publications since 1996, including 6 Books and 20 Additional arXiv Preprints 4 Contributions as Editor · 1 Further Contribution Co-Authors: 113 Co-Authors with 132 Joint Publications 3,121 Co-Co-Authors all top 5 Co-Authors 27 single-authored 15 Wirth, Fabian Roger 14 Worthmann, Karl 10 Semmler, Willi 9 Kellett, Christopher M. 8 Faulwasser, Timm 8 Pannek, Jürgen 8 Schaller, Manuel 7 Junge, Oliver 7 Kloeden, Peter Eris 6 Baumann, Michael Heinrich 6 Camilli, Fabio 6 Margaliot, Michael 6 Weller, Steven R. 5 Kriecherbauer, Thomas 5 Müller, Matthias A. 5 Nešić, Dragan 5 Schießl, Jonas 4 Allgower, Frank 4 Braun, Philipp 4 Krügel, Lisa 4 Ou, Ruchuan 4 Pirkelmann, Simon 4 Schiela, Anton 4 Stieler, Marleen 3 Baier, Robert 3 Falcone, Maurizio 3 Zidani, Hasnaa 2 Colonius, Fritz 2 Diehl, Moritz Mathias 2 Dower, Peter M. 2 Ferretti, Roberto Giorgio 2 Fleig, Arthur 2 Gaitsgory, Vladimir G. 2 Geiselhart, Roman 2 Guglielmi, Roberto 2 Hafstein, Sigurður Freyr 2 Kalise, Dante 2 Karafyllis, Iasson 2 Li, Huijuan 2 Lunze, Jan 2 Mechelli, Luca 2 Meurer, Thomas 2 Noroozi, Navid 2 Reble, Marcus 2 Seehafer, Martin 2 Sigurani, Manuela 2 Sontag, Eduardo D. 2 Volkwein, Stefan 2 Yegorov, Ivan V. 1 Altmüller, Nils 1 Andrej, Julian 1 Angeli, David 1 Aoyama, Hideaki 1 Bauer, Florian 1 Becker, Stephanie 1 Boccia, Andrea 1 Bock, Hans Georg 1 Bold, Lea 1 Botner, Meir 1 Caillau, Jean-Baptiste 1 Caraballo Garrido, Tomás 1 Cesaroni, Annalisa 1 Coron, Jean-Michel 1 Cyganowski, Sasha 1 Damm, Tobias 1 Eichfelder, Gabriele 1 Ernst, Andreas T. 1 Findeisen, Rolf 1 Fischer, Jörg 1 Fujiwara, Yoshi 1 Groß, Dominic 1 Hanebeck, Uwe D. 1 Hirche, Sandra 1 Höger, Matthias 1 Humaloja, Jukka-Pekka 1 Katz, Rami 1 Kern, Benjamin 1 Kliemann, Wolfgang H. 1 Köhler, Johannes 1 Kohler, Matthias 1 Koltai, Péter 1 Lehmann, Daniel 1 McEneaney, William “Mac” M. 1 Metscher, M. 1 Molin, Adam 1 Morris, Kirsten A. 1 Muff, David 1 Ofir, Ron 1 Ohlberger, Mario 1 Palma, Vryan Gil S. 1 Picarelli, Athena 1 Pinho, Maria Norberta 1 Pioch, Kilian 1 Rantzer, Anders 1 Rieger, Janosch 1 Rüffer, Björn Sebastian 1 Sager, Sebastian 1 Sailer, Rudolf 1 Saint-Pierre, Patrick 1 Saluzzi, Luca ...and 14 more Co-Authors all top 5 Serials 15 Systems & Control Letters 14 SIAM Journal on Control and Optimization 8 IEEE Transactions on Automatic Control 5 Automatica 5 Discrete and Continuous Dynamical Systems. Series B 5 Mathematical Control and Related Fields 4 Discrete and Continuous Dynamical Systems 3 Numerische Mathematik 3 Optimal Control Applications & Methods 3 Journal of Economic Dynamics & Control 2 Journal of Mathematical Analysis and Applications 2 Journal of Differential Equations 2 Journal of Optimization Theory and Applications 2 SIAM Journal on Numerical Analysis 2 Applied Numerical Mathematics 2 Computational Economics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Stochastics and Dynamics 2 GAMM-Mitteilungen 2 Journal of Computational Dynamics 2 Communications and Control Engineering 1 Computers & Mathematics with Applications 1 IMA Journal of Numerical Analysis 1 International Journal of Control 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Applied Mathematics and Optimization 1 BIT 1 Journal of Global Optimization 1 SIAM Review 1 Journal of Dynamics and Differential Equations 1 Computational Optimization and Applications 1 SIAM Journal on Scientific Computing 1 Economic Theory 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Difference Equations and Applications 1 Computing and Visualization in Science 1 Vietnam Journal of Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Nonlinear Analysis. Real World Applications 1 SIAM Journal on Applied Dynamical Systems 1 Oberwolfach Reports 1 Lecture Notes in Control and Information Sciences 1 Lecture Notes in Mathematics 1 Systems & Control: Foundations & Applications 1 Vieweg Studium 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Advances in Operations Research 1 Springer INdAM Series 1 Pure and Applied Functional Analysis 1 SpringerBriefs in Mathematics 1 Springer Studium Mathematik – Bachelor all top 5 Fields 107 Systems theory; control (93-XX) 58 Calculus of variations and optimal control; optimization (49-XX) 24 Numerical analysis (65-XX) 20 Ordinary differential equations (34-XX) 17 Operations research, mathematical programming (90-XX) 14 Partial differential equations (35-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Dynamical systems and ergodic theory (37-XX) 6 General and overarching topics; collections (00-XX) 6 Probability theory and stochastic processes (60-XX) 4 Computer science (68-XX) 2 History and biography (01-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 2 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 105 Publications have been cited 1,404 times in 763 Documents Cited by ▼ Year ▼ Nonlinear model predictive control. Theory and algorithms. Zbl 1220.93001 Grüne, Lars; Pannek, Jürgen 97 2011 Nonlinear model predictive control. Theory and algorithms. 2nd edition. Zbl 1429.93003 Grüne, Lars; Pannek, Jürgen 77 2017 Economic receding horizon control without terminal constraints. Zbl 1267.93052 Grüne, Lars 68 2013 An exponential turnpike theorem for dissipative discrete time optimal control problems. Zbl 1303.49013 Damm, Tobias; Grüne, Lars; Stieler, Marleen; Worthmann, Karl 52 2014 The dynamics of control. With an appendix by Lars Grüne. Zbl 1020.93500 Colonius, Fritz; Kliemann, Wolfgang 50 2000 Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. Zbl 1194.49045 Grüne, Lars 50 2009 Asymptotic behavior of dynamical and control systems under perturbation and discretization. Zbl 0991.37001 Grüne, Lars 47 2002 On the infinite horizon performance of receding horizon controllers. Zbl 1367.90109 Grüne, Lars; Rantzer, Anders 39 2008 Homogeneous state feedback stabilization of homogeneous systems. Zbl 0958.93077 Grüne, Lars 38 2000 Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation. Zbl 1115.93064 Nešić, Dragan; Grüne, Lars 38 2005 An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation. Zbl 0880.65045 Grüne, Lars 36 1997 On the relation between strict dissipativity and turnpike properties. Zbl 1335.93117 Grüne, Lars; Müller, Matthias A. 35 2016 Analysis of unconstrained nonlinear MPC schemes with time varying control horizon. Zbl 1208.49046 Grüne, Lars; Pannek, Jürgen; Seehafer, Martin; Worthmann, Karl 32 2010 Using dynamic programming with adaptive grid scheme for optimal control problems in economics. Zbl 1202.49026 Grüne, Lars; Semmler, Willi 32 2004 Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. Zbl 1436.49044 Grüne, Lars; Schaller, Manuel; Schiela, Anton 30 2020 Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models. Zbl 1044.93053 Grüne, Lars; Nesić, Dragan 29 2003 A generalization of Zubov’s method to perturbed systems. Zbl 1006.93061 Camilli, Fabio; Grüne, Lars; Wirth, Fabian 28 2001 Input-to-state dynamical stability and its Lyapunov function characterization. Zbl 1364.93567 Grüne, Lars 26 2002 Stability and feasibility of state constrained MPC without stabilizing terminal constraints. Zbl 1297.93068 Boccia, Andrea; Grüne, Lars; Worthmann, Karl 25 2014 Linear programming based Lyapunov function computation for differential inclusions. Zbl 1235.93222 Baier, Robert; Grüne, Lars; Hafstein, Sigurður Freyr 23 2012 Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems. Zbl 1387.49027 Grüne, Lars; Guglielmi, Roberto 23 2018 On the relation between discounted and average optimal value functions. Zbl 0918.49002 Grüne, Lars 21 1998 Pathwise approximation of random ordinary differential equations. Zbl 0998.65010 Grüne, L.; Kloeden, P. E. 21 2001 Higher order numerical schemes for affinely controlled nonlinear systems. Zbl 0992.65075 Grüne, L.; Kloeden, P. E. 19 2001 Periodic optimal control, dissipativity and MPC. Zbl 1369.93356 Zanon, Mario; Grüne, Lars; Diehl, Moritz 17 2017 Sensitivity analysis of optimal control for a class of parabolic PDEs motivated by model predictive control. Zbl 1420.49025 Grüne, Lars; Schaller, Manuel; Schiela, Anton 17 2019 Asymptotic controllability and exponential stabilization of nonlinear control systems at singular points. Zbl 0910.93063 Grüne, Lars 16 1998 Asymptotic stability equals exponential stability, and ISS equals finite energy gain – if you twist your eyes. Zbl 1043.93549 Grüne, Lars; Sontag, Eduardo D.; Wirth, Fabian R. 16 1999 Stabilization with discounted optimal control. Zbl 1327.93324 Gaitsgory, Vladimir; Grüne, Lars; Thatcher, Neil 14 2015 Control Lyapunov functions and Zubov’s method. Zbl 1157.93028 Camilli, Fabio; Grüne, Lars; Wirth, Fabian 13 2008 Approximation properties of receding horizon optimal control. Zbl 1336.93060 Grüne, Lars 13 2016 Global optimal control of perturbed systems. Zbl 1147.49019 Grüne, L.; Junge, O. 12 2008 Economic model predictive control without terminal constraints for optimal periodic behavior. Zbl 1339.93051 Müller, Matthias A.; Grüne, Lars 12 2016 Using nonlinear model predictive control for dynamic decision problems in economics. Zbl 1401.93094 Grüne, Lars; Semmler, Willi; Stieler, Marleen 12 2015 Distributed and boundary model predictive control for the heat equation. Zbl 1256.49033 Altmüller, Nils; Grüne, Lars 12 2012 A receding horizon control approach to sampled-data implementation of continuous-time controllers. Zbl 1100.93042 Nešić, Dragan; Grüne, Lars 11 2006 Continuous-time controller redesign for digital implementation: a trajectory based approach. Zbl 1138.93350 Grüne, Lars; Worthmann, Karl; Nešić, Dragan 10 2008 Asset pricing with loss aversion. Zbl 1181.91072 Grüne, Lars; Semmler, Willi 10 2008 Attraction rates, robustness, and discretization of attractors. Zbl 1058.65081 Grüne, Lars 10 2003 The role of sampling for stability and performance in unconstrained nonlinear model predictive control. Zbl 1292.93061 Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank 10 2014 Value iteration convergence of \(\varepsilon\)-monotone schemes for stationary Hamilton-Jacobi equations. Zbl 1334.65180 Bokanowski, Olivier; Falcone, Maurizio; Ferretti, Roberto; Grüne, Lars; Kalise, Dante; Zidani, Hasnaa 10 2015 ISS-Lyapunov functions for discontinuous discrete-time systems. Zbl 1360.93497 Grüne, Lars; Kellett, Christopher M. 10 2014 On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Zbl 1462.49058 Grüne, Lars; Guglielmi, Roberto 10 2021 Characterizing attraction probabilities via the stochastic Zubov equation. Zbl 1123.60311 Camilli, Fabio; Grüne, Lars 9 2003 Lyapunov’s second method for nonautonomous differential equations. Zbl 1128.37010 Grüne, Lars; Kloeden, Peter E.; Siegmund, Stefan; Wirth, Fabian R. 9 2007 Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. Zbl 0988.65077 Camilli, Fabio; Grüne, Lars 9 2000 A regularization of Zubov’s equation for robust domains of attraction. Zbl 1239.93048 Camilli, Fabio; Grüne, Lars; Wirth, Fabian 9 2001 Feedback stabilization methods for the numerical solution of ordinary differential equations. Zbl 1237.65085 Karafyllis, Iasson; Grüne, Lars 9 2011 A distributed NMPC scheme without stabilizing terminal constraints. Zbl 1328.93103 Grüne, Lars; Worthmann, Karl 9 2012 Turnpike properties in optimal control: an overview of discrete-time and continuous-time results. Zbl 1495.49019 Faulwasser, Timm; Grüne, Lars 9 2022 A uniform exponential spectrum for linear flows on vector bundles. Zbl 0983.37032 Grüne, Lars 8 2000 A set oriented approach to optimal feedback stabilization. Zbl 1129.93500 Grüne, Lars; Junge, Oliver 8 2005 Numerical stabilization of bilinear control systems. Zbl 0876.93032 Grüne, Lars 8 1996 Model predictive control, cost controllability, and homogeneity. Zbl 1453.93083 Coron, Jean-Michel; Grüne, Lars; Worthmann, Karl 8 2020 Stabilization of strictly dissipative discrete time systems with discounted optimal control. Zbl 1400.93267 Gaitsgory, Vladimir; Grüne, Lars; Höger, Matthias; Kellett, Christopher M.; Weller, Steven R. 8 2018 Comparing accuracy of second-order approximation and dynamic programming. Zbl 1282.91209 Becker, Stephanie; Grüne, Lars; Semmler, Willi 7 2007 Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation. Zbl 1074.65009 Grüne, Lars 7 2004 On the relation between turnpike properties for finite and infinite horizon optimal control problems. Zbl 1380.49055 Grüne, Lars; Kellett, Christopher M.; Weller, Steven R. 7 2017 A distributed optimization algorithm for the predictive control of smart grids. Zbl 1359.93270 Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl 7 2016 Higher order numerical approximation of switching systems. Zbl 1100.93022 Grüne, L.; Kloeden, P. E. 6 2006 Practical NMPC suboptimality estimates along trajectories. Zbl 1159.93013 Grüne, L.; Pannek, J. 6 2009 Discrete feedback stabilization of semilinear control systems. Zbl 0867.93071 Grüne, Lars 6 1996 Computation of local ISS Lyapunov functions with low gains via linear programming. Zbl 1366.37146 Li, Huijuan; Baier, Robert; Grüne, Lars; Hafstein, Sigurdur F.; Wirth, Fabian R. 6 2015 Nonconservative discrete-time ISS small-gain conditions for closed sets. Zbl 1395.93506 Noroozi, Navid; Geiselhart, Roman; Grüne, Lars; Rüffer, Björn S.; Wirth, Fabian R. 6 2018 Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. Zbl 1401.49035 Grüne, Lars; Pirkelmann, Simon; Stieler, Marleen 6 2018 Stabilization by sampled and discrete feedback with positive sampling rate. Zbl 0945.93604 Grüne, Lars 5 1999 Feedback stabilization of discrete-time homogeneous semi-linear systems. Zbl 0917.93058 Grüne, Lars; Wirth, Fabian 5 1999 Discretization, inflation and perturbation of attractors. Zbl 0996.37013 Grüne, L.; Kloeden, P. E. 5 2001 Economic model predictive control for time-varying system: performance and stability results. Zbl 1451.93095 Grüne, Lars; Pirkelmann, Simon 5 2020 Finite-dimensional output stabilization for a class of linear distributed parameter systems – a small-gain approach. Zbl 1492.93150 Grüne, L.; Meurer, T. 5 2022 Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. Zbl 1467.49037 Grüne, Lars; Schaller, Manuel; Schiela, Anton 5 2021 Model predictive control for nonlinear sampled-data systems. Zbl 1223.93081 Grüne, L.; Nešić, D.; Pannek, J. 4 2007 Differential games and Zubov’s method. Zbl 1237.49054 Grüne, Lars; Serea, Oana Silvia 4 2011 Stabilization of controlled diffusions and Zubov’s method. Zbl 1135.93033 Camilli, Fabio; Cesaroni, Annalisa; Grüne, Lars; Wirth, Fabian 4 2006 On numerical algorithm and interactive visualization for optimal control problems. Zbl 0970.65073 Grüne, L.; Metscher, M.; Ohlberger, M. 4 1999 Creditworthiness and thresholds in a credit market model with multiple equilibria. Zbl 1107.91361 Grüne, Lars; Semmler, Willi; Sieveking, Malte 4 2005 Strict dissipativity for discrete time discounted optimal control problems. Zbl 1481.49009 Grüne, Lars; Müller, Matthias A.; Kellett, Christopher M.; Weller, Steven R. 4 2021 Computing Lyapunov functions using deep neural networks. Zbl 1507.68267 Grüne, Lars 4 2021 Asset pricing with dynamic programming. Zbl 1161.91447 Grüne, Lars; Semmler, Willi 3 2007 Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations. Zbl 0948.93051 Grüne, Lars 3 1999 Maple for stochastic differential equations. Zbl 0991.65006 Cyganowski, S.; Grüne, L.; Kloeden, P. E. 3 2001 Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations. Zbl 1100.65056 Bauer, Florian; Grüne, Lars; Semmler, Willi 3 2006 Zubov’s equation for state-constrained perturbed nonlinear systems. Zbl 1322.93080 Grüne, Lars; Zidani, Hasnaa 3 2015 Zubov’s method for controlled diffusions with state constraints. Zbl 1323.93019 Grüne, Lars; Picarelli, Athena 3 2015 Simultaneously long short trading in discrete and continuous time. Zbl 1353.93116 Baumann, Michael Heinrich; Grüne, Lars 3 2017 Robustness of performance and stability for multistep and updated multistep MPC schemes. Zbl 1334.49099 Grüne, Lars; Palma, Vryan Gil 3 2015 Efficient model predictive control for parabolic PDEs with goal oriented error estimation. Zbl 1492.35391 Grüne, Lars; Schaller, Manuel; Schiela, Anton 3 2022 On approximating contractive systems. Zbl 1390.93186 Botner, Meir; Zarai, Yoram; Margaliot, Michael; Grüne, Lars 3 2017 Multiobjective model predictive control for stabilizing cost criteria. Zbl 1421.93050 Grüne, Lars; Stieler, Marleen 3 2019 On the rate of convergence of infinite horizon discounted optimal value functions. Zbl 0974.49002 Grüne, Lars; Wirth, Fabian 2 2000 Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations. Zbl 0988.65088 Grüne, Lars 2 2001 Computation of local ISS Lyapunov functions for discrete-time systems via linear programming. Zbl 1332.93328 Li, Huijuan; Grüne, Lars 2 2016 A double-sided dynamic programming approach to the minimum time problem and its numerical approximation. Zbl 1372.65193 Grüne, Lars; Le, Thuy T. T. 2 2017 Input-to-state stability, numerical dynamics and sampled-data control. Zbl 1196.93068 Grüne, Lars 2 2008 Dynamics, bifurcations, and control. 3rd nonlinear control workshop, Kloster Irsee, Germany, April 1–3, 2001. Zbl 0994.00036 2 2002 Numerical construction of nonsmooth control Lyapunov functions. Zbl 1414.93168 Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M. 2 2018 Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations. Zbl 1471.93084 Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan 2 2021 \(L^2\)-tracking of Gaussian distributions via model predictive control for the Fokker-Planck equation. Zbl 1406.35411 Fleig, Arthur; Grüne, Lars 2 2018 An invariance kernel representation of ISDS Lyapunov functions. Zbl 1100.93044 Grüne, Lars; Saint-Pierre, Patrick 1 2006 Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC. Zbl 07786395 Eichfelder, Gabriele; Grüne, Lars; Krügel, Lisa; Schießl, Jonas 1 2023 Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC. Zbl 07786395 Eichfelder, Gabriele; Grüne, Lars; Krügel, Lisa; Schießl, Jonas 1 2023 Turnpike properties in optimal control: an overview of discrete-time and continuous-time results. Zbl 1495.49019 Faulwasser, Timm; Grüne, Lars 9 2022 Finite-dimensional output stabilization for a class of linear distributed parameter systems – a small-gain approach. Zbl 1492.93150 Grüne, L.; Meurer, T. 5 2022 Efficient model predictive control for parabolic PDEs with goal oriented error estimation. Zbl 1492.35391 Grüne, Lars; Schaller, Manuel; Schiela, Anton 3 2022 Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation. Zbl 1524.65506 Andrej, Julian; Grüne, Lars; Mechelli, Luca; Meurer, Thomas; Pirkelmann, Simon; Volkwein, Stefan 1 2022 The interval turnpike property for adjoints. Zbl 1500.49011 Faulwasser, Timm; Grüne, Lars; Humaloja, Jukka-Pekka; Schaller, Manuel 1 2022 On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Zbl 1462.49058 Grüne, Lars; Guglielmi, Roberto 10 2021 Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. Zbl 1467.49037 Grüne, Lars; Schaller, Manuel; Schiela, Anton 5 2021 Strict dissipativity for discrete time discounted optimal control problems. Zbl 1481.49009 Grüne, Lars; Müller, Matthias A.; Kellett, Christopher M.; Weller, Steven R. 4 2021 Computing Lyapunov functions using deep neural networks. Zbl 1507.68267 Grüne, Lars 4 2021 Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations. Zbl 1471.93084 Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan 2 2021 Local turnpike analysis using local dissipativity for discrete time discounted optimal control. Zbl 1485.49032 Grüne, Lars; Krügel, Lisa 1 2021 (In-)stability of differential inclusions. Notions, equivalences, and Lyapunov-like characterizations. Zbl 1482.34002 Braun, Philipp; Grüne, Lars; Kellett, Christopher M. 1 2021 Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. Zbl 1436.49044 Grüne, Lars; Schaller, Manuel; Schiela, Anton 30 2020 Model predictive control, cost controllability, and homogeneity. Zbl 1453.93083 Coron, Jean-Michel; Grüne, Lars; Worthmann, Karl 8 2020 Economic model predictive control for time-varying system: performance and stability results. Zbl 1451.93095 Grüne, Lars; Pirkelmann, Simon 5 2020 Sensitivity analysis of optimal control for a class of parabolic PDEs motivated by model predictive control. Zbl 1420.49025 Grüne, Lars; Schaller, Manuel; Schiela, Anton 17 2019 Multiobjective model predictive control for stabilizing cost criteria. Zbl 1421.93050 Grüne, Lars; Stieler, Marleen 3 2019 Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems. Zbl 1387.49027 Grüne, Lars; Guglielmi, Roberto 23 2018 Stabilization of strictly dissipative discrete time systems with discounted optimal control. Zbl 1400.93267 Gaitsgory, Vladimir; Grüne, Lars; Höger, Matthias; Kellett, Christopher M.; Weller, Steven R. 8 2018 Nonconservative discrete-time ISS small-gain conditions for closed sets. Zbl 1395.93506 Noroozi, Navid; Geiselhart, Roman; Grüne, Lars; Rüffer, Björn S.; Wirth, Fabian R. 6 2018 Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. Zbl 1401.49035 Grüne, Lars; Pirkelmann, Simon; Stieler, Marleen 6 2018 Numerical construction of nonsmooth control Lyapunov functions. Zbl 1414.93168 Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M. 2 2018 \(L^2\)-tracking of Gaussian distributions via model predictive control for the Fokker-Planck equation. Zbl 1406.35411 Fleig, Arthur; Grüne, Lars 2 2018 Nonlinear model predictive control. Theory and algorithms. 2nd edition. Zbl 1429.93003 Grüne, Lars; Pannek, Jürgen 77 2017 Periodic optimal control, dissipativity and MPC. Zbl 1369.93356 Zanon, Mario; Grüne, Lars; Diehl, Moritz 17 2017 On the relation between turnpike properties for finite and infinite horizon optimal control problems. Zbl 1380.49055 Grüne, Lars; Kellett, Christopher M.; Weller, Steven R. 7 2017 Simultaneously long short trading in discrete and continuous time. Zbl 1353.93116 Baumann, Michael Heinrich; Grüne, Lars 3 2017 On approximating contractive systems. Zbl 1390.93186 Botner, Meir; Zarai, Yoram; Margaliot, Michael; Grüne, Lars 3 2017 A double-sided dynamic programming approach to the minimum time problem and its numerical approximation. Zbl 1372.65193 Grüne, Lars; Le, Thuy T. T. 2 2017 On the relation between strict dissipativity and turnpike properties. Zbl 1335.93117 Grüne, Lars; Müller, Matthias A. 35 2016 Approximation properties of receding horizon optimal control. Zbl 1336.93060 Grüne, Lars 13 2016 Economic model predictive control without terminal constraints for optimal periodic behavior. Zbl 1339.93051 Müller, Matthias A.; Grüne, Lars 12 2016 A distributed optimization algorithm for the predictive control of smart grids. Zbl 1359.93270 Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl 7 2016 Computation of local ISS Lyapunov functions for discrete-time systems via linear programming. Zbl 1332.93328 Li, Huijuan; Grüne, Lars 2 2016 Stabilization with discounted optimal control. Zbl 1327.93324 Gaitsgory, Vladimir; Grüne, Lars; Thatcher, Neil 14 2015 Using nonlinear model predictive control for dynamic decision problems in economics. Zbl 1401.93094 Grüne, Lars; Semmler, Willi; Stieler, Marleen 12 2015 Value iteration convergence of \(\varepsilon\)-monotone schemes for stationary Hamilton-Jacobi equations. Zbl 1334.65180 Bokanowski, Olivier; Falcone, Maurizio; Ferretti, Roberto; Grüne, Lars; Kalise, Dante; Zidani, Hasnaa 10 2015 Computation of local ISS Lyapunov functions with low gains via linear programming. Zbl 1366.37146 Li, Huijuan; Baier, Robert; Grüne, Lars; Hafstein, Sigurdur F.; Wirth, Fabian R. 6 2015 Zubov’s equation for state-constrained perturbed nonlinear systems. Zbl 1322.93080 Grüne, Lars; Zidani, Hasnaa 3 2015 Zubov’s method for controlled diffusions with state constraints. Zbl 1323.93019 Grüne, Lars; Picarelli, Athena 3 2015 Robustness of performance and stability for multistep and updated multistep MPC schemes. Zbl 1334.49099 Grüne, Lars; Palma, Vryan Gil 3 2015 An exponential turnpike theorem for dissipative discrete time optimal control problems. Zbl 1303.49013 Damm, Tobias; Grüne, Lars; Stieler, Marleen; Worthmann, Karl 52 2014 Stability and feasibility of state constrained MPC without stabilizing terminal constraints. Zbl 1297.93068 Boccia, Andrea; Grüne, Lars; Worthmann, Karl 25 2014 The role of sampling for stability and performance in unconstrained nonlinear model predictive control. Zbl 1292.93061 Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank 10 2014 ISS-Lyapunov functions for discontinuous discrete-time systems. Zbl 1360.93497 Grüne, Lars; Kellett, Christopher M. 10 2014 Economic receding horizon control without terminal constraints. Zbl 1267.93052 Grüne, Lars 68 2013 Linear programming based Lyapunov function computation for differential inclusions. Zbl 1235.93222 Baier, Robert; Grüne, Lars; Hafstein, Sigurður Freyr 23 2012 Distributed and boundary model predictive control for the heat equation. Zbl 1256.49033 Altmüller, Nils; Grüne, Lars 12 2012 A distributed NMPC scheme without stabilizing terminal constraints. Zbl 1328.93103 Grüne, Lars; Worthmann, Karl 9 2012 Nonlinear model predictive control. Theory and algorithms. Zbl 1220.93001 Grüne, Lars; Pannek, Jürgen 97 2011 Feedback stabilization methods for the numerical solution of ordinary differential equations. Zbl 1237.65085 Karafyllis, Iasson; Grüne, Lars 9 2011 Differential games and Zubov’s method. Zbl 1237.49054 Grüne, Lars; Serea, Oana Silvia 4 2011 Analysis of unconstrained nonlinear MPC schemes with time varying control horizon. Zbl 1208.49046 Grüne, Lars; Pannek, Jürgen; Seehafer, Martin; Worthmann, Karl 32 2010 Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. Zbl 1194.49045 Grüne, Lars 50 2009 Practical NMPC suboptimality estimates along trajectories. Zbl 1159.93013 Grüne, L.; Pannek, J. 6 2009 On the infinite horizon performance of receding horizon controllers. Zbl 1367.90109 Grüne, Lars; Rantzer, Anders 39 2008 Control Lyapunov functions and Zubov’s method. Zbl 1157.93028 Camilli, Fabio; Grüne, Lars; Wirth, Fabian 13 2008 Global optimal control of perturbed systems. Zbl 1147.49019 Grüne, L.; Junge, O. 12 2008 Continuous-time controller redesign for digital implementation: a trajectory based approach. Zbl 1138.93350 Grüne, Lars; Worthmann, Karl; Nešić, Dragan 10 2008 Asset pricing with loss aversion. Zbl 1181.91072 Grüne, Lars; Semmler, Willi 10 2008 Input-to-state stability, numerical dynamics and sampled-data control. Zbl 1196.93068 Grüne, Lars 2 2008 Lyapunov’s second method for nonautonomous differential equations. Zbl 1128.37010 Grüne, Lars; Kloeden, Peter E.; Siegmund, Stefan; Wirth, Fabian R. 9 2007 Comparing accuracy of second-order approximation and dynamic programming. Zbl 1282.91209 Becker, Stephanie; Grüne, Lars; Semmler, Willi 7 2007 Model predictive control for nonlinear sampled-data systems. Zbl 1223.93081 Grüne, L.; Nešić, D.; Pannek, J. 4 2007 Asset pricing with dynamic programming. Zbl 1161.91447 Grüne, Lars; Semmler, Willi 3 2007 Default risk, asset pricing, and debt control. Zbl 1418.91586 Grüne, Lars; Semmler, Willi 1 2007 A receding horizon control approach to sampled-data implementation of continuous-time controllers. Zbl 1100.93042 Nešić, Dragan; Grüne, Lars 11 2006 Higher order numerical approximation of switching systems. Zbl 1100.93022 Grüne, L.; Kloeden, P. E. 6 2006 Stabilization of controlled diffusions and Zubov’s method. Zbl 1135.93033 Camilli, Fabio; Cesaroni, Annalisa; Grüne, Lars; Wirth, Fabian 4 2006 Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations. Zbl 1100.65056 Bauer, Florian; Grüne, Lars; Semmler, Willi 3 2006 An invariance kernel representation of ISDS Lyapunov functions. Zbl 1100.93044 Grüne, Lars; Saint-Pierre, Patrick 1 2006 Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation. Zbl 1115.93064 Nešić, Dragan; Grüne, Lars 38 2005 A set oriented approach to optimal feedback stabilization. Zbl 1129.93500 Grüne, Lars; Junge, Oliver 8 2005 Creditworthiness and thresholds in a credit market model with multiple equilibria. Zbl 1107.91361 Grüne, Lars; Semmler, Willi; Sieveking, Malte 4 2005 Using dynamic programming with adaptive grid scheme for optimal control problems in economics. Zbl 1202.49026 Grüne, Lars; Semmler, Willi 32 2004 Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation. Zbl 1074.65009 Grüne, Lars 7 2004 Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models. Zbl 1044.93053 Grüne, Lars; Nesić, Dragan 29 2003 Attraction rates, robustness, and discretization of attractors. Zbl 1058.65081 Grüne, Lars 10 2003 Characterizing attraction probabilities via the stochastic Zubov equation. Zbl 1123.60311 Camilli, Fabio; Grüne, Lars 9 2003 Asymptotic behavior of dynamical and control systems under perturbation and discretization. Zbl 0991.37001 Grüne, Lars 47 2002 Input-to-state dynamical stability and its Lyapunov function characterization. Zbl 1364.93567 Grüne, Lars 26 2002 Dynamics, bifurcations, and control. 3rd nonlinear control workshop, Kloster Irsee, Germany, April 1–3, 2001. Zbl 0994.00036 2 2002 A generalization of Zubov’s method to perturbed systems. Zbl 1006.93061 Camilli, Fabio; Grüne, Lars; Wirth, Fabian 28 2001 Pathwise approximation of random ordinary differential equations. Zbl 0998.65010 Grüne, L.; Kloeden, P. E. 21 2001 Higher order numerical schemes for affinely controlled nonlinear systems. Zbl 0992.65075 Grüne, L.; Kloeden, P. E. 19 2001 A regularization of Zubov’s equation for robust domains of attraction. Zbl 1239.93048 Camilli, Fabio; Grüne, Lars; Wirth, Fabian 9 2001 Discretization, inflation and perturbation of attractors. Zbl 0996.37013 Grüne, L.; Kloeden, P. E. 5 2001 Maple for stochastic differential equations. Zbl 0991.65006 Cyganowski, S.; Grüne, L.; Kloeden, P. E. 3 2001 Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations. Zbl 0988.65088 Grüne, Lars 2 2001 The dynamics of control. With an appendix by Lars Grüne. Zbl 1020.93500 Colonius, Fritz; Kliemann, Wolfgang 50 2000 Homogeneous state feedback stabilization of homogeneous systems. Zbl 0958.93077 Grüne, Lars 38 2000 Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. Zbl 0988.65077 Camilli, Fabio; Grüne, Lars 9 2000 A uniform exponential spectrum for linear flows on vector bundles. Zbl 0983.37032 Grüne, Lars 8 2000 On the rate of convergence of infinite horizon discounted optimal value functions. Zbl 0974.49002 Grüne, Lars; Wirth, Fabian 2 2000 Asymptotic stability equals exponential stability, and ISS equals finite energy gain – if you twist your eyes. Zbl 1043.93549 Grüne, Lars; Sontag, Eduardo D.; Wirth, Fabian R. 16 1999 Stabilization by sampled and discrete feedback with positive sampling rate. Zbl 0945.93604 Grüne, Lars 5 1999 Feedback stabilization of discrete-time homogeneous semi-linear systems. Zbl 0917.93058 Grüne, Lars; Wirth, Fabian 5 1999 On numerical algorithm and interactive visualization for optimal control problems. Zbl 0970.65073 Grüne, L.; Metscher, M.; Ohlberger, M. 4 1999 Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations. Zbl 0948.93051 Grüne, Lars 3 1999 ...and 5 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,158 Authors 64 Grüne, Lars 20 Worthmann, Karl 19 Hafstein, Sigurður Freyr 19 Kloeden, Peter Eris 17 Giesl, Peter 17 Müller, Matthias A. 16 Semmler, Willi 15 Wirth, Fabian Roger 14 Karafyllis, Iasson 14 Kellett, Christopher M. 14 Zuazua, Enrique 13 Efimov, Denis V. 13 Polyakov, Andrey 11 Allgower, Frank 10 Dashkovskiy, Sergey N. 10 Faulwasser, Timm 10 Gaitsgory, Vladimir G. 9 Kunisch, Karl 9 Mironchenko, Andrii 8 Gugat, Martin 8 Houska, Boris 8 Sanchez, Tonametl 8 Schaller, Manuel 7 Alla, Alessandro 7 Borzì, Alfio 7 Falcone, Maurizio 7 Li, Huijuan 7 Pepe, Pierdomenico 6 Azmi, Behzad 6 Colonius, Fritz 6 Jiang, Zhong-Ping 6 Junge, Oliver 6 Kawan, Christoph 6 Kolmanovsky, Ilya V. 6 Nešić, Dragan 6 Peitz, Sebastian 6 Picarelli, Athena 6 Teel, Andrew Richard 6 Trélat, Emmanuel 6 Veliov, Vladimir M. 6 Volkwein, Stefan 5 Angeli, David 5 Annunziato, Mario 5 Asai, Yusuke 5 Geiselhart, Roman 5 Kalise, Dante 5 Lhachemi, Hugo 5 Malisoff, Michael 5 Moreno, Jaime A. 5 Noroozi, Navid 5 Pannek, Jürgen 5 Schiela, Anton 5 Shvartsman, Ilya A. 5 Weller, Steven R. 5 Zanon, Mario 4 Albi, Giacomo 4 Baier, Robert 4 Carbonell, Felix 4 Dimarogonas, Dimos V. 4 Dower, Peter M. 4 Flaßkamp, Kathrin 4 Gerdts, Matthias 4 Goreac, Dan 4 Graichen, Knut 4 Grundel, Sara M. 4 Herty, Michael Matthias 4 Jentzen, Arnulf 4 Jimenez, Juan Carlos 4 Jones, Colin Neil 4 Khlopin, Dmitriĭ Valer’evich 4 Krstić, Miroslav 4 Lazar, Mircea 4 Mehrez, Mohamed W. 4 Naujok, Lars 4 Novara, Carlo 4 Perruquetti, Wilfrid 4 Prieur, Christophe 4 Rasmussen, Martin 4 Zidani, Hasnaa 3 Ahmed-Ali, Tarek 3 Alamir, Mazen 3 Anitescu, Mihai 3 Atolia, Manoj 3 Bock, Hans Georg 3 Borkar, Vivek Shripad 3 Bourdin, Loïc 3 Camilli, Fabio 3 Chaillet, Antoine 3 Chatterjee, Debasish 3 Dai, Hao 3 Dawid, Herbert 3 de Queiroz, Marcio S. 3 Dhar, Gaurav 3 Di Ferdinando, Mario 3 Elaiw, Ahmed M. 3 Fečkan, Michal 3 Fridman, Emilia 3 Geshkovski, Borjan 3 Gray, W. Steven 3 Gros, Sebastien ...and 1,058 more Authors all top 5 Cited in 157 Serials 132 Automatica 53 Systems & Control Letters 34 SIAM Journal on Control and Optimization 26 International Journal of Control 22 MCSS. Mathematics of Control, Signals, and Systems 22 European Journal of Control 21 International Journal of Robust and Nonlinear Control 16 Journal of the Franklin Institute 16 Journal of Optimization Theory and Applications 14 Journal of Economic Dynamics & Control 12 Journal of Mathematical Analysis and Applications 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 10 Discrete and Continuous Dynamical Systems. Series B 9 Journal of Differential Equations 9 Optimal Control Applications & Methods 9 Mathematical Control and Related Fields 9 Journal of Computational Dynamics 8 Discrete and Continuous Dynamical Systems 7 Applied Mathematics and Optimization 7 Journal of Computational and Applied Mathematics 7 SIAM Journal on Scientific Computing 7 Journal of Difference Equations and Applications 7 Nonlinear Dynamics 6 Applied Mathematics and Computation 6 Numerische Mathematik 6 Mathematical Problems in Engineering 6 Communications in Nonlinear Science and Numerical Simulation 6 Nonlinear Analysis. Hybrid Systems 6 International Journal of Systems Science. Principles and Applications of Systems and Integration 5 Computers & Mathematics with Applications 5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Journal of Computational Physics 4 Journal of Scientific Computing 4 Journal of Dynamics and Differential Equations 4 Computational Optimization and Applications 4 Computational Economics 4 Optimization Methods & Software 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 Mathematical and Computer Modelling of Dynamical Systems 4 Journal of Systems Science and Complexity 4 Stochastics and Dynamics 4 GAMM-Mitteilungen 3 BIT 3 Computing 3 Physica D 3 Applied Numerical Mathematics 3 International Journal of Adaptive Control and Signal Processing 3 Numerical Algorithms 3 Advances in Computational Mathematics 3 Complexity 3 SIAM Journal on Applied Dynamical Systems 3 Oberwolfach Reports 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Dynamic Games and Applications 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Chaos, Solitons and Fractals 2 Canadian Mathematical Bulletin 2 Information Sciences 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Numerical Analysis 2 Applied Mathematical Modelling 2 Automation and Remote Control 2 SIAM Journal on Optimization 2 Differential Equations and Dynamical Systems 2 Vietnam Journal of Mathematics 2 Chaos 2 Optimization and Engineering 2 Lobachevskii Journal of Mathematics 2 Differential Equations 2 Computational Management Science 2 Advances in Difference Equations 2 Journal of Control Science and Engineering 2 Asian Journal of Control 2 Journal of Theoretical Biology 2 Evolution Equations and Control Theory 2 Vestnik KRAUNTS. Fiziko-Matematicheskie Nauki 1 Artificial Intelligence 1 Journal of Mathematical Biology 1 Mathematical Methods in the Applied Sciences 1 Nonlinearity 1 Ukrainian Mathematical Journal 1 Journal of Theoretical and Applied Mechanics (Sofia) 1 Hokkaido Mathematical Journal 1 International Journal for Numerical Methods in Engineering 1 Journal of Approximation Theory 1 Journal of Economic Theory 1 Metroeconomica 1 Naval Research Logistics 1 Operations Research 1 Studies in Applied Mathematics 1 Chinese Annals of Mathematics. Series B 1 Stochastic Analysis and Applications 1 Optimization 1 Queueing Systems 1 Science in China. Series A 1 Neural Networks 1 European Journal of Applied Mathematics 1 Real-Time Systems 1 Neural Computation ...and 57 more Serials all top 5 Cited in 40 Fields 513 Systems theory; control (93-XX) 193 Calculus of variations and optimal control; optimization (49-XX) 100 Numerical analysis (65-XX) 86 Ordinary differential equations (34-XX) 84 Operations research, mathematical programming (90-XX) 76 Partial differential equations (35-XX) 68 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 63 Dynamical systems and ergodic theory (37-XX) 37 Probability theory and stochastic processes (60-XX) 28 Biology and other natural sciences (92-XX) 15 Difference and functional equations (39-XX) 15 Computer science (68-XX) 10 Mechanics of particles and systems (70-XX) 10 Fluid mechanics (76-XX) 7 Operator theory (47-XX) 7 Statistics (62-XX) 6 Information and communication theory, circuits (94-XX) 5 General and overarching topics; collections (00-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Sequences, series, summability (40-XX) 3 General topology (54-XX) 3 Mechanics of deformable solids (74-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Combinatorics (05-XX) 2 Approximations and expansions (41-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.