Prescribed-time Control With Time-varying Output Constraints For A Class Of Nonlinear Systems

It is known that nonlinearities are inescapable in any practical systems,such as robots,aerospace systems,and spring-mass-damper systems,and the nonlinear systems have drawn considerable attention.Switched systems have drawn considerable attention over the past few years.A large number of practical systems also can be modeled as switched systems,such as chemical systems,traffic systems,and robot systems.In practical applications,there is an increasing demand for control performance,asymptotic convergence,finite time convergence depending on initial conditions,is no longer sufficient.On the other hand,the performance requirements and safety needs have been taken into account,the steady-state performance,overshoot,convergence time and convergence speed of the system need to meet certain constraints according to the expected demand.In other words,the system is required to guarantee the achievement of the predefined performance.How to ensure that a nonlinear system can achieve certain predefined performance within a finite time,which can be set arbitrarily,is the focus of this paper.In this paper,the problems of prescribed time control with time-varying output constraints for a class of nonlinear systems and a class of switched nonlinear systems are investigatedThe main research contents are as follows:In Chapter 1,nonlinear systems,nonlinear switching systems,finite-time stability,and performance control problems are reviewed respectively.In Chapter 2,the prescribed-time tracking with time-varying output constraints for a class of nonlinear systems is studied.Firstly,by introducing a convergence-invariant unbounded transformation,a new transformed system is given by incorporating the prescribed performance bounds into the original system.Secondly,the control law is designed by backstepping technique with the quadratic Lyapunov function,in which a fractional term plays a significant role in accomplish prescribed-time tracking with guaranteed transient performance.Then,the prescribed-time tracking with time-varying output constraints is achieved,and the output tracking error converges to zero within prescribed-time and remains at equilibrium thereafter,while the boundedness of all closed-loop signals is assured.Finally,two examples are given to illustrate the effectiveness of the proposed results.In Chapter 3,the problem of the prescribed-time stabilization for a class of switched nonlinear systems with time-varying output constraints is studied.First,a new coordinate design of the output enables the constraints to be incorporated into the original system.Secondly,a fractional term will be played an essential role in achieving prescribedtime stabilization.Then,based on the method of Barrier Lyapunov function(BLF)and backstepping,a recursive algorithm is developed to construct a controller to achieve the prescribed-time stabilization with time-varying output constraints.Finally,two examples are provided to show the effectiveness of the proposed results.In Chapter 4,the main research work of the paper is summarized,and looks forward to the next research work and direction.