Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

Yongfeng Lv, Jing Na*, Qinmin Yang, Xing Wu, Yu Guo

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

82 Citations (Scopus)
371 Downloads (Pure)


An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.

Original languageEnglish
Pages (from-to)99-112
Number of pages14
JournalInternational Journal of Control
Issue number1
Early online date31 Jul 2015
Publication statusPublished - Jan 2016


  • adaptive control
  • approximate dynamic programming
  • nonlinear systems
  • optimal control
  • system identification

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