Fault-Tolerant Control Of Nonlinear Systems Based On Adaptive Dynamic Programming

With the advancement of science and technology,systems are becoming more complicated and the scales of systems are becoming larger and larger.Therefore,faults in systems occur more frequently,and system faults may lead to system performance degradation or system instability,resulting in property damage or even personal injury security.Therefore,the study of fault-tolerant control is very important,and the addition of adaptive dynamic programming method can enable the system to maintain a certain performance when the system faults occur.Based on the adaptive dynamic programming method,this paper studies the following contents for the fault-tolerant control of nonlinear systems:(1)For the tracking problem of a class of nonlinear systems with actuator faults,the system is transformed at first,and the steady-state part of the controller is designed based on the original system without faults and the reference trajectory,and the optimal tracking control problem is transformed to optimal stabilization control problem.Then a novel performance index function is constructed by adding a part that reflects the actuator fault to the conventional performance index function.An adaptive law is designed to estimate actuator faults.With the approximation performance of neural networks,a neural network with a single hidden layer is developed as a critic neural network,and the weights of the neural network are updated by the gradient descent method to approximate the performance index function.The approximate optimal feedback control is obtained from the critic neural network.The approximation errors of the neural network weights and the tracking errors of closed-loop system are uniformly ultimately bounded.The effectiveness of the designed controller is verified by numerical simulation.(2)For a class of nonlinear system tracking problem with actuator faults and bounded disturbance,the system is firstly transformed,and the steady-state part of the controller is designed based on the original system without fault and disturbance and the reference trajectory.The optimal tracking control problem is transformed into an optimal stabilization control problem.Then the adaptive law is designed to estimate actuator faults.A novel performance index function that can reflect tracking error,control input,and actuator faults is designed.By utilizing the approximation feature of the neural network,a neural network with a single hidden layer constitutes the critic neural network.The weights of the neural network are updated by the gradient descent method to approximate the performance index function,and the approximate optimal controller is directly obtained from the critic neural network.Disturbance compensation controller is added to feedback part of the controller to deal with the impact of disturbance on the system.The approximation errors of the neural network weights and the tracking errors of closed-loop system are uniformly ultimately bounded.The effectiveness of the designed controller is verified by numerical simulation.(3)For the problem of stabilization of a class of nonlinear systems with sensor faults,the state observer is designed to estimate the states of the system,and it is proved that the estimation errors are uniformly ultimately bounded.Then the neural network is used to approximate the performance index function and approximately optimal feedback control can be obtained directly from the critic neural network.It is proved that the neural network weight approximation errors are uniformly ultimately bounded,and that the state trajectories of the closed-loop system are uniformly ultimately bounded.The effectiveness of the designed controller is verified by numerical simulation.