Online adaptive approximate optimal tracking control with simplified dual approximation structure for continuous-time unknown nonlinear systems

Jing Na*, Guido Herrmann

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

84 Citations (Scopus)

Abstract

This paper proposes an online adaptive approximate solution for the infinite-horizon optimal tracking control problem of continuous-time nonlinear systems with unknown dynamics. The requirement of the complete knowledge of system dynamics is avoided by employing an adaptive identifier in conjunction with a novel adaptive law, such that the estimated identifier weights converge to a small neighborhood of their ideal values. An adaptive steady-state controller is developed to maintain the desired tracking performance at the steady-state, and an adaptive optimal controller is designed to stabilize the tracking error dynamics in an optimal manner. For this purpose, a critic neural network (NN) is utilized to approximate the optimal value function of the Hamilton-Jacobi-Bellman (HJB) equation, which is used in the construction of the optimal controller. The learning of two NNs, i.e., the identifier NN and the critic NN, is continuous and simultaneous by means of a novel adaptive law design methodology based on the parameter estimation error. Stability of the whole system consisting of the identifier NN, the critic NN and the optimal tracking control is guaranteed using Lyapunov theory; convergence to a near-optimal control law is proved. Simulation results exemplify the effectiveness of the proposed method.

Original languageEnglish
Article number7004668
Pages (from-to)412-422
Number of pages11
JournalIEEE/CAA Journal of Automatica Sinica
Volume1
Issue number4
DOIs
Publication statusPublished - 1 Oct 2014

Keywords

  • Adaptive control
  • approximate dynamic programming
  • optimal control
  • system identification

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  • Prizes

    Hsue-shen Tsien Paper Award of IEEE/CAA Journal of Automatica Sinica

    Jing Na (Recipient) & Guido Herrmann (Recipient), Jan 2018

    Prize: Prizes, Medals, Awards and Grants

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