Tracking Control For Strict-feedback Nonlinear Systems

Generally speaking,the practical engineering systems are almost nonlinear systems,it is very meaningful to study the nonlinear systems.Recently,the control methods for nonlinear system have made great progress,where the backstepping-based design method received a lot of attention.Based on the current research findings on the control of strict-feedback nonlinear systems,and by using backstepping technology,fault-tolerant control theory and stochastic theory,this paper studies the adaptive output feedback fault-tolerant control problem for a class of strict-feedback uncertain nonlinear systems and the decentralized tracking control problem for a class of interconnected stochastic nonlinear systems.First of all,the problem of adaptive fault-tolerant control is considered for a class of strict-feedback uncertain nonlinear systems,where the nonlinear functions are allowed to include the unmeasured states.On the one hand,considering the continue nonlinear systems,by introducing a high-gain observer,the states and parameters can be estimated accurately.By combining the estimated states and switching fault-tolerant strategy,and based on a series of monitoring functions,the fault-tolerant control scheme is proposed,which can ensure the tracking error within the prescribed performance regardless the faults.On the other hand,considering the sampled nonlinear system,a sampled observer is introduced to estimate the states and parameters.Here,the prescribed performance bounds are selected as the monitoring functions to detect the faults,and the designed switching fault-tolerant method can guarantee the tracking error converge to an adjustable neighbourhood of the origin eventually both in the fault free case and faulty case.By using Lyapunov stability theory,it is proved that all the signals in the closed-loop systems are bounds and the tracking error satisfies the desirable tracking performance.Secondly,the problem of tracking control is considered for a class of interconnected stochastic nonlinear systems,where the interconnections are allowed to include the states of each subsystem.Considering the stochastic systems with matching interconnections,a new decentralized control method is proposed,where a modified compensation mechanism is presented to address the unknown interconnections and the adaptive control laws based on the smooth switching function are designed.Subsequently,extending the result of the matching case to the mismatching case,and introducing the adaptive control laws and compensation mechanisms to each virtual control to compensate the unknown interconnections.Under the two cases,by using quartic Lyapunov functions and graph theory,it is proven that the resulting closed-loop system signals are bounded,and the tracking errors converge to a compact set,whose radius can be adjustable by choosing different controller design parameters.Finally,for the considered two class of strict-feedback nonlinear systems,the examples are given to illustrate the effectiveness of the proposed methods.