Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems

Weinan Gao, Zhong-Ping Jiang

Research output: Contribution to journalArticle

Abstract

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any $a$ $priori$ knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

Original languageEnglish (US)
JournalIEEE Transactions on Neural Networks and Learning Systems
DOIs
StateAccepted/In press - Nov 7 2017

Fingerprint

Dynamic programming
Nonlinear systems
Feedback
Iterative methods
Dynamical systems
Stabilization

Keywords

  • Adaptation models
  • Adaptive dynamic programming (ADP)
  • adaptive optimal tracking
  • Adaptive systems
  • Convergence
  • Dynamic programming
  • Learning systems
  • Mathematical model
  • Nonlinear systems
  • optimal control
  • uncertain nonlinear systems.

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

Cite this

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abstract = "This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any $a$ $priori$ knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.",
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