The Optimal Control Of Nonlinear Systems Based On Adaptive Dynamic Programming

In practical engineering applications,the existence of environmental factors and various artificial factors results in different degrees of nonlinear characteristics in control systems.These nonlinear characteristics may lead to a decrease in system performance or instability.Therefore,it is necessary to study the optimal control problem of nonlinear systems to ensure the normal operation of the system.In recent years,the optimal control problem of nonlinear systems has been one of the hot topics in academic research.Adaptive Dynamic Programming(ADP)is one of the effective methods to solve the optimal control problem.It can help us to solve the problem faster,improve computational efficiency,and reduce costs when dealing with nonlinear optimal control problems.Therefore,it is of great significance to study the optimal control problem of nonlinear systems based on adaptive dynamic programming.This article studies the optimal control problem of nonlinear systems based on event-triggered adaptive dynamic programming method.The main research content is divided into the following three parts:1)This article studies the optimal control problem of nonlinear systems in the presence of external disturbances and proposes an optimal control strategy based on event-triggered adaptive dynamic programming techniques.Firstly,a nonlinear quadratic value function is defined to optimize the system’s performance,and the corresponding Hamilton-Jacobi(HJ)equation is established.Based on the Bellman principle,the optimal control strategy and the worst disturbance strategy are obtained.In order to reduce the update frequency of the control strategy and disturbance strategy,an event-triggered update mechanism is introduced and an event-triggered threshold is designed.The stability of the system is proved using the Lyapunov method.Then,an evaluation-execution neural network model is established to approximate the performance index function and control strategy.The evaluation network is used to approximate the performance index function,and the two execution networks respectively approximate the control input and external disturbance.The weight update rules of the evaluation network and execution network are given using the least squares method.Finally,the effectiveness of the proposed algorithm is verified through a simulation example.2)This article studies the optimal control problem of nonlinear systems based on the eventtriggered adaptive dynamic programming method in the presence of external disturbances and state constraints.First,a discrete-time system described by differential equations containing external disturbances and state constraints is established.Then,a barrier function is designed to ensure the safety and optimality of the system,and a performance index function including the barrier function is given.Second,the Hamilton-Jacobi(HJ)equation is proposed,and the optimal control strategy and worst-case disturbance strategy are obtained based on the Bellman principle.In order to avoid the resource consumption caused by periodic data transmission and communication,an eventtriggered mechanism is introduced in the system,and the stability of the system is proved by using the Lyapunov function.Finally,a suitable evaluation-execution neural network structure model is established to approximate the performance index function and the optimal control strategy.The effectiveness of the proposed algorithm is verified through simulation using matlab tools.3)This article studied the hierarchical optimization control problem of nonlinear systems and proposed a hierarchical optimization control strategy based on adaptive dynamic programming.Firstly,the HJ equation was proposed,and the coupled form of two HJB equations was established based on the Bellman principle,and the optimal control strategies of the two players were separately solved.Then,it was proved that the solutions of these two equations not only stabilized the system,but also constituted a Stackelberg equilibrium strategy.Next,a value iteration algorithm was proposed to solve the control strategy,and an evaluation neural network was used to approximate the value function,and the least squares method was used to update the weight of the neural network.Finally,the validity of the algorithm was demonstrated through examples.This article studies the optimal control problem of several types of nonlinear systems based on adaptive dynamic programming.At the same time,the stability of closed-loop systems and the convergence of algorithms are analyzed.