Optimal Control Method For Nonlinear Systems With Resource Efficient Utilization

Over the past decades,researchers have developed a variety of control methods to stabilize nonlinear systems based on classical control,modern control and intelligent control theories.However,the stabilization is only the basic requirement of the control design in practical applications.Optimal control not only can achieve this goal,but also has optimality.Adaptive dynamic programming(ADP)which integrates dynamic programming,reinforcement learning and neural network techniques can avoid the “curse of dimensionality” in solving optimal control problem,and has widely applied to solve robust control,differential game,fault tolerant control problems and so on.With the increasingly complex systems,a large amount of data needs to be calculated,how to improve the usage of computation and communication resources needs further research under the limited hardware performance.This thesis investigates the optimal control method for nonlinear systems with resource efficient utilization.The main contributions and works of this thesis are summarized as the following aspects.(1)Considering a class of input-constrained nonlinear systems with internal dynamics and input matrix uncertainties,this thesis develops an ADP-based event-triggered robust control method.To begin with,the robust control problem is transformed into an optimal control problem by designing a modified value function composed of system state,control input and two known upper-bound functions for nominal system.Then,a critic-only strategy is introduced to approximate optimal value function and obtain optimal control law.In order to improve the usage rate of computation and communication resources,an event-triggering threshold is derived based on Lyapunov stability theorem to determine whether the control law should be updated or not,and the threshold can guarantee the closed-loop system to be uniformly ultimately bounded(UUB).(2)To handle the zero-sum game(ZSG)problems of unknown nonlinear multi-player systems,an observer-based event-triggered control method is developed by using ADP in this thesis.By employing online input and output data,a neural network observer is designed to identify the system dynamics and relax the requirement of system dynamics.Furthermore,based on the critic-only structure,the Hamilton-Jacobi-Issacs equation of ZSG can be solved,and the optimal control law and the worst disturbance law can be obtain.To improve the usage of computation and communication resources,all controls are updated when events occur according to a design event-triggered threshold.Moreover,Lyapunov stability theorem is employed to prove that the the closed-loop system is UUB.(3)To address the nonzero-sum game problems of the uncertain nonlinear multi-player systems,an improved event-triggered robust control method is developed by using ADP.First,by constructing an auxiliary systems and designing a novel value function,the robust control problem is converted to an optimal control problem.Then,a critic neural network is employed to approximate the value function of each player for solving Hamilton-Jacobi(HJ)equation,then the optimal control law and optimal auxiliary control law are obtained.Under the eventtriggered mechanism,these control laws are all updated when event occur.Thus,the computational burden is reduced,the communication resource is saved.According to Lyapunov stability theorem,the closed-loop system state is guaranteed to be UUB.(4)Considering a class of nonlinear interconnected systems with actuator failures,an ADP-based event-triggered decentralized integral sliding mode control method is developed to solve the fault tolerant control problem.Long time system operation may lead to the occurrence of faults inevitably,which will not only reduce the service life of plants,but even cause serious consequences.To address the actuator failures,for each subsystem,a discontinuous control law is employed to maintain the subsystem state on sliding mode surface,eliminate the effect of actuator failures and obtain the sliding mode dynamics.Then,an event-triggered optimal control law is designed to guarantee the stability of the sliding mode dynamics by using ADP technique and event-triggered mechanism,and the control law is updated when events occur.The proposed method can decrease the updating frequency of the event-triggered optimal control law,reduce the computational burden,and save communication resource.Furthermore,based on the experience replay technique,a modified critic neural network updating policy is presented to relax the persistence of excitation condition by using the history data.According to the Lyapunov stability theorem,we prove that the closed-loop system is asymptotically stable.(5)An event-triggered integral sliding mode control method for an uncertain macro-micro composite stage(MMCS)system with actuator failures.In this system,the macro-micro motion controlled by two controllers is important for the fast and precise positioning,i.e.,the highspeed macro-motion realized via the voice coil motor,and the high-precision micro-motion via the piezoelectric device.However,these two motions influence each other,which increases the difficulty of control design.In this thesis,the MMCS system is regarded as a two-player system,where two cooperative players guarantee the system to be stable with different control cost,and this problem is formulated as a nonzero-sum game problem.Meanwhile,actuator failures are considered in this thesis.To begin with,an integral sliding mode control method is developed to eliminate the effect of the actuator failures and the uncertainties,then the nominal MMCS system is obtained.Then,an ADP-based event-triggered optimal control scheme is developed to solve the nonzero-sum game problem of the nominal MMCS system.Critic-only strategy is employed to approximate the coupled value function for solving event-triggered HJ equation and obtain the optimal control law for each player.Furthermore,we prove that the closed-loop MMCS system is asymptotically stable by using Lyapunov stability theorem.Finally,the conclusion and the future works are presented to end the thesis.