Stable Tracking Control Of Nonlinear Systems With Asymmetric Non-smooth Constrained Inputs

Most of the control inputs in the actual engineer systems are asymmetric non-smooth saturation forms,and the parameters in engineer systems are uncertain.Engineer systems in the long run process will inevitably occur failure problems.Considering the above problems exist in most engineer systems,this paper studied parametric uncertain nonlinear systems for asymmetric non-smooth saturation and actuator faults in depth.Firstly,we studied normal form high-order nonlinear systems with asymmetric non-smooth saturation and actuator faults.The two scheme,robust adaptive controller and fault-tolerant controller,are designed for this two kinds of nonlinear systems.In this work,a well-defined asymmetric smooth function is introduced,which is used to approximate the non-smooth saturation function.The two control algorithms are designed to deal with the problem of asymmetric non-smooth saturation and actuator faults.Unlike most existing control schemes for high-order nonlinear systems,most schemes need to assume that the control gain is an unknown constant.However,the controllers designed in this paper only need the control gain be a bounded unknown time-varying function.In this work,the controllers can guarantee that all signals of the closed-loop system are global unified bounded,which are strictly proved by the Lyapunov stability analysis methods.The simulation results show the effectiveness of the proposed control schemes.Secondly,another kind of strict-feedback nonlinear systems with asymmetric non-smooth saturation and actuator faults are studied and discussed.Then,a robust adaptive DSC tracking controller and a fault-tolerant controller are designed for this type of systems.In this work,three well-defined asymmetric smooth functions are introduced,which were used to approximate the saturation function.At the same time,a Nussbaum type function was introduced to solve the problem that control gain which is difficult to be controlled because it is unknown and time-varying.The control algorithms,which,as compared with the existing methods,exhibits several attractive features such as,dealing with strict feedback systems with time-varying unknown control gain and parametric uncertainties;coping with asymmetric and non-smooth input saturation without requiring the prior knowledge of bound of input saturation;accommodating unexpected actuation faults;and structurally simple andcomputationally inexpensive.The proposed control schemes can guarantee all of the signals in the closed-loop system are semi-globally uniformly ultimate bounded.Finally,a simulation experiment is utilized to demonstrate the feasibility of the proposed approaches.The proposed design methods can effectively solve all kinds of parameter uncertain nonlinear systems with asymmetric non-smooth saturation and actuator faults.This paper has solved the problem of stable tracking control for normal form high-order nonlinear systems and strict feedback nonlinear systems under the multiple uncertainties.such as,Asymmetric non-smooth saturation input,external perturbation,bounded time-varying control gain,parameter uncertainty and actuator failure.Finally,the limitations of the research contents of this paper are discussed,and the general reversal of these systems is given in view of these problems.