Finite Time Backstepping Control Of Uncertain Nonlinear Systems With Asymmetric Constraints And Application

In recent years,the control of uncertain nonlinear systems have been developed rapidly.Many kinds of nonlinear control methods have been proposed by domestic and foreign scholars.Finite time control has attracted more and more attention due to its fast convergence speed and high tracking accuracy.At the same time,it has been widely used in many fields.In this paper,the control problem of uncertain nonlinear system with asymmetric constraints?external disturbances?uncertainty and actuator faults is proposed.The main contents are as follows:Firstly,a finite time back-stepping control strategy is proposed for a nonlinear systems with output constraints and external disturbances.An asymmetric barrier function is used to deal with the output constraints problem.A fixed time disturbance observer is used to estimate the external disturbance,and the estimation error converges to zero in fixed time.The controller is designed by back-stepping control strategy.Based on Lyapunov stability theory,the closed-loop system is proved to be bounded stable in finite time.And the output of the system satisfies the constraints.The effectiveness of the control strategy is verified by an application example of a permanent magnet synchronous motor system.Secondly,an adaptive fixed time back-stepping control strategy is designed for an uncertain nonlinear system with output constraints and external disturbances.The output constraint problem of the system is solved by using an asymmetric log-type barrier Lyapunov function.A fixed-time disturbance observer is designed to estimate external disturbances.An adaptive fixed time filter is designed to solve the problem of “term of explosion” in traditional back-stepping control.And the unknown upper bound of the derivative of virtual control input is estimated by an adaptive law.The closed-loop system is proved to be bounded stable in fixed time by combining Lyapunov stability theory.The effectiveness of the control strategy is verified by an application example of a permanent magnet synchronous motor system.Finally,a fixed time fault-tolerant controller is designed for the tracking control problem of uncertain nonlinear systems under the comprehensive influence of full state constraints,uncertainty and actuator faults.A state transition function is introduced to solve the full state constraints of the system.The uncertainty is estimated based on radial basis function neural networks.An adaptive law is used to eliminate the influence of actuator failure.Based on this,combined with back-stepping control,a fixed time fault-tolerant control strategy is designed.Lyapunov stability theory is used to prove that the closed-loop system is bounded stable in fixed time.The effectiveness of the designed control strategy is verified by an application example of a permanent magnet synchronous motor system.