Research On Event-triggered Optimal Control Of Nonlinear System

The traditional control task is time-triggered.It refers to sampling the state information of the system in a fixed time interval and making the sampled signal enter the closed-loop system.This may result in poor control performance due to bandwidth constraints on the network.Recently,event-triggered control has gained wide interest in the field of control for its advantages of reducing the transmission burden,saving communication and improving computational efficiency.Its control input is only updated when the triggering condition is violated,which reduces the average update frequency of the actuator.The traditional event triggered control hardly considers the optimal control.Optimization refers to the ability to maximize control performance and minimize control resources.Finding the optimal controller is equivalent to solving the HJB equation.For nonlinear systems,it is not easy to solve this partial differential equations.With the development of neural network,ADP can effectively solve the optimal control problem of nonlinear system.In this paper,ADP technology and event-triggered control method are effectively combined to achieve the purpose of saving communication resources.The main contents of this paper are as follows.Firstly,an event-triggered approximate optimal control structure is proposed for nonlinear continuous systems with control constraints.Aiming at the saturated actuator,the non-quadratic cost function is established,and the HJB equation of constrained nonlinear system is introduced.The critic network is used to estimate the cost function,and the actor network is used to approximate the optimal control law of the nonlinear system.By using Lyapunov method,the triggering conditions are derived under the condition of guaranteeing the ultimate boundedness of the closed-loop system.Simulation results show that the system is ultimately uniformly bounded.Secondly,the event-triggered adaptive optimal control of nonlinear systems based on unmeasurable states is studied.The observer based on neural network is used to learn the system state by event-triggered method.At the same time,the action-critic network structure is used to learn the cost function and optimal control law.Through the Lyapunov stability criterion,the ultimate boundedness of the closed-loop system is guaranteed.Through simulation,it can be found that the observer can accurately simulate the real-time state trajectory of the unmeasurable state system.Finally,a new event-triggered control strategy is proposed for continuous-time nonlinear systems with unknown disturbances.By introducing the infinite integral cost function of the nominal system,the event-triggered nonlinear control problem is transformed into the event triggered nonlinear optimal control problem.Then,recurrent neural network and adaptive critic design methods are used to solve the derived event-triggered nonlinear optimal control problem.By using Lyapunov method,it is proved that the system state is ultimately uniformly bounded under the designed triggering condition.Simulation results show that the proposed event-triggered method can improve the utilization efficiency of communication resources.