Approximate optimal tracking control for continuous-time unknown nonlinear systems

Jing Na*, Yongfeng Lv, Xing Wu, Yu Guo, Qiang Chen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

13 Citations (Scopus)


This paper proposes an online adaptive approximate solution for the infinite-horizon optimal tracking control for continuous-time nonlinear systems with unknown system dynamics, which is achieved in terms of a novel identifier-critic based approximate dynamic programming (ADP) structure. To obviate the requirement of complete knowledge of system dynamics, an adaptive neural network (NN) identifier is designed with a novel adaptive law. A steady-state control in conjunction with an adaptive optimal control is proposed to stabilize the tracking error dynamics in an optimal manner. A critic NN is utilized to approximate the optimal value function and to obtain the optimal control action. Novel adaptive laws based on parameter estimation error are developed to guarantee that both the identifier NN weights and critic NN weights converge to small neighborhoods of their ideal values. The closed-loop system stability and the convergence to the optimal solution are all proved based on Lyapunov theory. Simulation results exemplify the efficacy of the proposed methods.

Original languageEnglish
Title of host publicationChinese Control Conference, CCC
PublisherIEEE Computer Society
Number of pages6
ISBN (Print)9789881563842
Publication statusPublished - 1 Jan 2014
Event33rd Chinese Control Conference, CCC 2014 - Nanjing, United Kingdom
Duration: 28 Jul 201430 Jul 2014


Conference33rd Chinese Control Conference, CCC 2014
Country/TerritoryUnited Kingdom


  • Adaptive control
  • Approximate dynamic programming
  • Optimal control
  • System identification


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