Prescribed Performance Backstepping Control Of Uncertain Nonlinear System

In recent years,the control of nonlinear system has been received more and more atten-tion and has achieved remarkable results.The prescribed performance control can make the performance of the control system reach the preset requirements,and ensure that the track-ing error converges to any small bounded neighborhood set in advance,so the research on the prescribed performance control has been applied to many fields.This paper proposes a new prescribed performance control strategy for the control problem of a class of nonlin-ear systems with external disturbances or parameter uncertainties.The main contents are as follows.Firstly,a prescribed performance backstepping control strategy is designed for the track-ing control problems of a class of nonlinear systems with external disturbances.A barrier Lyapunov function is designed to guarantee the prescribed performance of the system;con-sidering the external disturbance and the derivative of the virtual control input as lumped uncertainty,and designing the disturbance observer to estimate it,thus avoiding the problem of "term of explosion" in traditional backstepping control;the actual control input is de-signed under the backstepping framework.The stability of the system is proved by Lyapunov theory,the stable tracking of the system output is realized and the output tracking error satis-fies the preset transient and steady-state performance.The simulation of permanent magnet synchronous motor proves the effectiveness of the proposed control strategy.Secondly,for a class of nonlinear systems with uncertainties,the control strategy is designed combine adaptive backstepping control with filter.The adaptive law is used to es-timate the upper bound of uncertainty;in order to avoid the problem of "term of explosion”in traditional backsteppinbg control,a novel filter is designed to estimate the time derivative of the virtual control input,and the actual control input is designed under the backstepping framework.It is proved by Lyapunov theory that the system is uniformly bounded,the sta-ble tracking of the system output is achieved and the output tracking error satisfies the preset transient and steady state performance.The effectiveness of the designed control scheme is proved by the simulation of flexible hypersonic vehicle.Finally,a new prescribed performance backstepping control scheme is proposed for a class of nonlinear systems with unknown parameters and external disturbance.A novel barrier Lyapunov function is designed to ensure the prescribed performance of tracking error;the adaptive law is used to estimate the unknown parameters,and the disturbance observer is designed to estimate the external disturbance in the system.In order to avoid the problem of“term of explosion”problem in traditional backstepping control,a new first-order filter is designed to estimate the time derivative of the virtual control inputs.Based on this,the backstepping controller is designed.On the basis of the Lyapunov theory,the stability of the closed-loop system and the prescribed performance of the tracking error are proved.The effectiveness of the control strategy is verified by the simulation of the permanent magnet synchronous motor system.