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A novel neural network discrete‐time optimal control design for nonlinear time‐delay systems using adaptive critic designs
Author(s) -
Liang Yuling,
Zhang Huaguang,
Zhang Kun,
Wang Rui
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2567
Subject(s) - artificial neural network , control theory (sociology) , nonlinear system , computer science , discrete time and continuous time , adaptive control , lyapunov function , norm (philosophy) , optimal control , control (management) , mathematical optimization , mathematics , artificial intelligence , statistics , physics , quantum mechanics , political science , law
Summary In this article, a novel neural network (NN) optimal control approach using adaptive critic designs is developed for nonlinear discrete‐time (DT) systems with time delays. First, to eliminate the delay term of control input, a time‐delay matrix function is developed by designing a M network. Furthermore, the cost function is approximated by the critic NN, and the control signal can be obtained directly by using the information of critic NN according to the equilibrium condition. In addition, to shorten the learning time and reduce the computational burden in the control process, a novel control strategy with less adjustable parameters for the time‐delay DT nonlinear systems is proposed in this article, in which the norm of the weight estimations of critic NN is updated to generate a novel long‐term performance function. The proposed control algorithm using adaptive critic designs has the advantage of reducing adaptive learning parameters and lessening calculative burden. The Lyapunov stability analysis shows that the time‐delay DT controlled systems can be uniformly ultimately bounded stable. Finally, three simulations are presented to demonstrate the control performance of the developedmethod.