Adaptive Compensation Control For An Infinite Number Of Actuator Failure

It is well known that in real life,the control problem of the system is often complicated.Exter-nal interference,system uncertainty,actuator failures and other uncertain factors will cause great changes in system parameters,which may lead to system performance degradation,system insta-bility and even catastrophic accidents.Therefore,the research on compensation of actuator failures is of both theoretical and practical significance,especially for some life-critical systems such as aircrafts and manned spacecraft.In recent years,many researchers have devoted themselves to the research of compensation control for nonlinear systems,and have achieved some important research results,most of which are aimed at nonlinear systems with finite actuator failures.In real life,the system is usually vulnerable to infinite actuator failures.Therefore,adaptive compensa-tion control for nonlinear systems with infinite number of actuator failures and uncertainties are addressed in this paper,mainly including:1.Adaptive state feedback compensation control for nonlinear systemsAn adaptive state feedback compensation control scheme is proposed for nonlinear systems with infinite actuator failures.Compensating for infinite number of actuator failures based on the tuning function approach is an important but challenging problem in the field of adaptive con-trol.Combining the smooth projection operator and tuning function method,the jumping size of Lyapunov function at each failure instant can be ensured bounded.By finding the minimum time interval between two successive failures,the sudden increase of the Lyapunov function at failure instant can be offset by the continuous decline in this time interval.Therefore,the accumulation of infinite jumps will not lead to the ceaseless increase of Lyapunov function,ensuring the bounded-ness of Lyapunov function.Finally,all closed-loop system signals are uniformly bounded and the tracking error converges to a small neighborhood around origin.The tracking error can converge to origin when the actuator failure occurs only a finite number of times.In this part,an explicit bound for L₂norm of tracking error is also given.Finally,the effectiveness of the design control scheme is verified by simulations.2.Adaptive output feedback compensation control for nonlinear systemsBy using bound estimation method,Nussbaum function,K-filters and higher-order Lyapunov function,an adaptive output feedback compensation control scheme for nonlinear systems with infinite actuator failures and uncertainties is proposed.Firstly,a parametric model with unknown system uncertainty and infinite number of actuator failures is established in our manuscript,in which the additive fault is modeled as the combination of unknown constants and known bounded scalar signals with unknown weights,so good simulation performance is obtained.Secondly,the bounds of a part of uncertainties have been estimated,and the rest part has been dealt by Nussbaum function,so it can guarantee the Lyapunov function constructed at each step has no jump when the fault occurs.Then the high-order Lyapunov function is proposed,which solves the problems en-countered in using the Nussbaum function.This scheme ensures that all closed-loop signals are globally uniformly bounded,and the tracking error converges to a small residue set.Finally,the effectiveness of the design scheme is verified by simulations.