Optimal Control Of Nonlinear Systems With Time Delays Based On Adaptive Dynamic Programming Approach

Time-delay exists widely in various industrial control systems and communication networks.It may cause poor dynamic performance and poor robustness,or even lead to the collapse of the system in some cases,resulting in huge loss of life and property.Therefore,the study on the stability,robustness and control performance of time-delay systems has important theoretical and application value.At the same time,considering that there are certain control constraints in the application of most practical systems,the controller designed without considering the control constraints will bring unexpected problems in applications.Based on this,this paper focuses on the stability and optimal control of nonlinear time-delay systems.Furthermore,we also consider the control performance and optimal control problems of nonlinear time-delay systems with saturated actuator constraints,which have important theoretical significance and application value.In this paper,the online ADP method based on neural network is used to study the optimal control problem of time-delay and nonlinear systems with control constraints.The main results of the paper are as follows:1.Given a class of nonlinear systems with time-delay,the online ADP algorithm is used to solve the continuous HJB equation by using two BP neural networks to approximate the control input and performance index function simultaneously.On this basis,the correlation optimal control problem under infinite time is studied.Finally,numerical simulation results show that the controller works well and the proposed algorithm is effective.2.Given a class of nonlinear systems with time-delay and saturated actuator.We define a new performance index function effectively to measure the control constraints.Then,we obtain the optimal control input signal based on online ADP algorithm.Besides,it is convenient and effective to adopt a single BP neural network to approximate the optimal control input and performance index function at the same time.Numerical simulations verify the effectiveness of the algorithm.3.As for the above two systems,the effects of the stability condition and the delay parameter on the system are discussed by the second method of Lyapunov theorem,and the proof is provided in detail.For different BP neural networks,the convergence of the weights of neural networks is verified respectively.In addition,the simulation results show that the optimal control law designed in this paper can stabilize the system and the weights of neural networks are convergent.