zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Optimal probability density function control for NARMAX stochastic systems. (English) Zbl 1149.93350
Summary: This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output Probability Density Function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.

93E20Optimal stochastic control (systems)
93C10Nonlinear control systems
93E15Stochastic stability
Full Text: DOI
[1] Astrom, K. J.: Introduction to stochastic control theory, (1970)
[2] Clark, D. W.: Advances in model-based predictive control, (1994) · Zbl 0825.93403
[3] Crespo, L. G.; Sun, J. Q.: Non-linear stochastic control via stationary response design, Probabilistic engineering mechanics 18, 73-86 (2003)
[4] Crowley, T. J.; Meadows, E. S.; Kostoulas, E.; Iii, F. J. Doyle: Control of particle size distribution described by a population balance model of semibatch emulsion polymerisation, Journal of process control 10, 419-432 (2000)
[5] Forbes, M. G., Forbes, J. F., & Guay, M. (2003). Regulatory control design for stochastic processes: Shaping the probability density function. In Proc. ACC’2003 (pp. 3998-4003)
[6] Guo, L.; Wang, H.: PID controller design for output pdfs of stochastic systems using linear matrix inequalities, IEEE transactions on systems, man and cybernetics-part B 35, 65-71 (2005)
[7] Lavretsky, E. (2000). Greedy optimal control. In Proc. ACC’2000 (pp. 3888-3892)
[8] Papoulis, A.: Probability, random variables and stochastic processes, (1991) · Zbl 0191.46704
[9] Petersen, I. R.; James, M. R.; Dupuis, P.: Minimax optimal control of stochastic uncertain systems with relative entropy constraints, IEEE transactions on automatic control 45, 398-412 (2000) · Zbl 0978.93083 · doi:10.1109/9.847720
[10] Wang, H.: Bounded dynamic stochastic systems: modelling and control, (2000) · Zbl 0938.93001
[11] Wang, H.: Control of conditional output probability density functions for general nonlinear and non-Gaussian dynamic stochastic systems, IEE Proceedings part D: Control theory & application 150, 55-60 (2003)
[12] Yue, H.; Wang, H.: Minimum entropy control of closed loop tracking errors for dynamic stochastic systems, IEEE transactions on automatic control 48, 118-122 (2003)