Optimal Control For Continuous Time Nonlinear Systems With State Delays

For a long time,the problem of optimal control for nonlinear continuous time systems with state delay is one of the hot topics in the control field,strategy iterative algorithm is an effective method to solve the optimal control problems in approximate dynamic programming theory.Based on this method,the optimal control and tracking problems of nonlinear continuous time systems with state delay are studied in this paper.Firstly,for the optimal control problem,considering the influence of state delay on the system,a new performance index function in the infinite time domain is defined,and the online actorcritic algorithm is used to solve the nonlinear HJB equation in real time,which is called synchronous strategy iterative algorithm.The neural network technology is used to realize the algorithm,and the critic network and the actor network are tuned at the same time to obtain the new weight update rates with the term of state delay,and then the optimal control is realized.Secondly,for the tracking control problem,the system is transformed into a tracking error system,and the performance index function is defined to be composed of state error,delay state error and control error.The HJB equation is solved by using both policy iterative algorithm and neural network theory,and the iterative update rate of the performance index function and tracking control is obtained.Then,the convergence of the policy iterative algorithm is proved strictly based on Lyapunov analysis method,meanwhile the stability of the system can be guaranteed.Finally,the effectiveness of the theoretical results is demonstrated by numerical examples.