Tracking Control for Nonlinear Nonparametric Systems Based on the Stochastic Approximation Algorithm

In this article, we study the tracking control problem for nonlinear nonparametric systems, and additive random observation noise is also taken into account. The dynamical function is allowed to be time varying and possess an arbitrary growth rate at control input. The control algorithm is designed...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 68; H. 1; S. 230 - 241
Hauptverfasser: Feng, Wenhui, Zhao, Shixin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Approximation
Approximation algorithms
Control systems
Control theory
Convergence
Heuristic algorithms
Mathematical analysis
Nonlinear control
Nonlinear system
Nonlinear systems
Nonparametric statistics
nonparametric system
Physics
Regulators
stochastic approximation (SA)
Tracking control
Upper bound
ISSN:0018-9286, 1558-2523
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Abstract In this article, we study the tracking control problem for nonlinear nonparametric systems, and additive random observation noise is also taken into account. The dynamical function is allowed to be time varying and possess an arbitrary growth rate at control input. The control algorithm is designed on the basis of the stochastic approximation algorithm with expanding truncations, and it is found that there is a tradeoff between the growth rate of the dynamical function at control input and that of the truncation bound sequence to be chosen. We prove that the average tracking or strong tracking is asymptotically achieved for a class of reference state sequences, which can be strongly averaged. Finally, numerical simulations given in this article justify the theoretical assertions.
AbstractList In this article, we study the tracking control problem for nonlinear nonparametric systems, and additive random observation noise is also taken into account. The dynamical function is allowed to be time varying and possess an arbitrary growth rate at control input. The control algorithm is designed on the basis of the stochastic approximation algorithm with expanding truncations, and it is found that there is a tradeoff between the growth rate of the dynamical function at control input and that of the truncation bound sequence to be chosen. We prove that the average tracking or strong tracking is asymptotically achieved for a class of reference state sequences, which can be strongly averaged. Finally, numerical simulations given in this article justify the theoretical assertions.
Author Feng, Wenhui
Zhao, Shixin
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  organization: Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China
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SubjectTerms Algorithms
Approximation
Approximation algorithms
Control systems
Control theory
Convergence
Heuristic algorithms
Mathematical analysis
Nonlinear control
Nonlinear system
Nonlinear systems
Nonparametric statistics
nonparametric system
Physics
Regulators
stochastic approximation (SA)
Tracking control
Upper bound
Title Tracking Control for Nonlinear Nonparametric Systems Based on the Stochastic Approximation Algorithm
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