Prescribed Finite-Time Stabilization And Tracking Control Design For A Class Of Nonlinear Systems

With the rapid development of human society,various high-tech fields are also making continuous progress,such as machinery,aerospace and other fields,which is all related with control design.Most of them are researches on nonlinear systems in essence.At the same time,the controlled objects in the cutting-edge fields of artificial intelligence and intelligent robots are becoming more and more complex,and people have higher and higher requirements for system performance.For the stability analysis and tracking control design of complex nonlinear systems,basic methods are difficult to solve the problem.Therefore,in the field of control,the study of nonlinear systems with constraints has received more and more attention.In the past researches,when designing the controllers,the designer only controlled the tracking error in a very small range in an infinite time,or the designed setting time depends on the initial conditions and parameters,and the designer cannot arbitrarily set the time to stabilize the system state.At the same time,how to ensure that the system is controlled in the time-varying output constraint and stable within a prescribed time is also the content we need to study.This paper proposes a novel recursive design algorithm to help general nonlinear systems or uncertain nonlinear systems achieve performance optimization,and develop system control theory.And here are the main contents of the paper as follows:The Chapter 1 provides a basic explanation of nonlinear system theory,tracking control theory,finite-time stability.In this chapter,we provides a basic overview of the concept,research significance of tracking control theory and system performance,and expounds a large number of topics related to finite-time stability of nonlinear systems in recent years,as well as aspects of finite-time stability that need to be studied.In the Chapter 2,the prescribed-time tracking with prescribed performance for a class of strict-feedback nonlinear systems is investigated.This chapter proposes a control strategy to achieve the tracking error constrain by the prescribed performance bounds(PPB),and the tracking error converges to zero in prescribed time.The PPB not only constrains the convergence rate,but also constrains the maximum overshoot of the tracking error.And such a design makes the prescribed time independent of the initial conditions and design parameters.Firstly,by incorporating the PPB into the original system via a transformation,and a transformed system is obtained,which is unconstrained and convenient for controlling the design.Then,through the backstepping technique,the controller is designed by recursion method to ensure that the tracking error satisfies the PPB all the time,and converges to zero in prescribed time.The key to designing the controller is that a fractional term is introduced when designing the virtual stabilizing function during each step of backstepping,which in turn decreases the Lyapunov function to origin within prescribed-time.Finally,two examples verify the effectiveness of the controller designed in this chapter.Chapter 3 shows the problem of prescribed-time stabilization for a class of uncertain nonlinear systems with full-state constraints.First,we use time-varying coordinate transformations to combine the constraint function with the original system.Next,the barrier Lyapunov function(BLF)and backstepping technique are applied to achieve prescribed-time stabilization by adding a score term to the transformed system,which can reduce the BLF to the origin at any designed time,so as to achieve prescribed-time stabilization,and the method of adding score terms plays an important role in system stability.Then,we propose an analysis of prescribed-time stabilization with state constraints.Finally,the effectiveness of the designed controller is proved by an example.The main feature of this chapter is that the setting time of system is independent of parameters,nor does it depend on the initial conditions,and it can be set arbitrarily according to our wishes,giving the system good performance.The other is that all states of the uncertain system are constrained.Chapter 4 mainly summarizes the research content of the paper and looks forward to the research direction in future.