Optimal Control Design Of Nonlinear Systems Based On Single-network Adaptive Dynamic Programming

For the analytical study of modern control systems,the optimal control problem has attracted much attention.On the one hand,ensuring the closed-loop stability of the controlled systems is just the minimum requirement,further optimizing system performance is desirable;on the other hand,many classical optimal control methods are not suitable for solving the optimal control problems of complex nonlinear systems.In order to improve traditional methods and achieve the optimal control of increasingly complex nonlinear systems,adaptive dynamic programming(ADP)method is proposed.ADP method combined with reinforcement learning and dynamic programming(DP)algorithm provides a new control strategy for nonlinear systems optimal control.In addition,the existing researches on the optimal control of uncertain nonlinear systems with multiple complex constraints are not still complete.All industrial systems are inevitably restricted by their own or external constraints,the optimal control of uncertain nonlinear systems under multiple complex constraints becomes more important.Therefore,based on the single-network ADP method,this paper proposes adaptive optimal controller design schemes for several uncertain nonlinear systems with different constraints.The main contents are as follows:(1)The adaptive optimal control problem of strict feedback nonlinear systems with prescribed performance and input dead zone is investigated.The design process of the controller includes two parts: the feedforward controller and the optimal feedback controller.In the first part,the prescribed performance function is introduced,which reduces the dependence on experience of selecting controller design parameters,and ensures that the convergence trajectory of the tracking error satisfies the requirements of the prescribed performance.A simplified dead-zone model based on the dead-zone slope parameters is used to overcome the difficulties of controller design.In the second part,for the auxiliary affine error system,the single-network ADP algorithm based on fuzzy logic systems is used to approximate the optimal cost function,and the requirement of the initial admissible controller is relaxed by introducing robust items.Through theoretical analysis,it is proved that the closed-loop system is uniformly ultimately bounded(UUB).The simulation example verifies the effectiveness of the proposed method.(2)Considering an uncertain nonlinear systems with partial failure of actuators,the problem of event-driven guaranteed cost optimal tracking controller design is explored.In order to complete the tracking task of system states,an augmented system composed of error system and reference system is first constructed.With the help of a modified discount cost function,the system uncertainties and actuator faults are taken into account.Then,single-network ADP method is used to achieve approximate event-triggered optimal controller design.The event-triggered manner proposed is dynamic,which is different from static trigger manner.It can promote execution efficiency under the action of the internal dynamic signal.The Lyapunov method theoretically guarantees that the closed-loop system is UUB.(3)Distributed optimal attitude synchronization control problem is addressed for multiple quad-rotor unmanned aerial vehicles(UAVs)with attitude constraints,input saturation,uncertain model and external disturbances.By introducing nonlinear mapping based on barrier functions,the constrained systems are transformed into new equivalent unconstrained ones.The model uncertainties and unknown external disturbances are approximated by disturbance observers with local states.For each UAV,an improved non-quadratic cost function is constructed to reflect simultaneously the requirement of robust performance and the constraints of control input.Hereafter,single-network ADP algorithm is utilized to derive the optimal control policy.Concurrent learning technique relaxes the persistence of excitation(PE)condition by training the critic neural networks with both historical and current state data.Finally,the attitude system consensus errors and the critic neural network weight evaluation errors are proved to be UUB.Simulation results of attitude systems of quad-rotor UAVs show the effectiveness of the proposed algorithm.