Finite Time Optimal Stabilization Control Design For Constrained Nonlinear Systems

Predictive control is called model predictive control.It has developed rapidly in recent years because that it possesses the merit of handling input and state constraints of systems,but the condition of most algorithms can run is that the optimization problem is assumed to be feasible,and the specific description of the feasible area cannot be given.So there has been a way to combine Lyapunov functions method with predictive control,it can not only consider the performance of the system sufficiently,but also give the description of the initial feasible region.In the practical application of industry,many systems require that the states can converge to the equilibrium point in finite time.So it is necessary to study the finite time stabilization of nonlinear systems by using the predictive control method based on the Lyapunov function.In this paper,a predictive control method based on Lyapunov function is used to stabilize a class of nonlinear systems with input and state constraints,nonlinear systems with constraints and external perturbations and a class of nonlinear switched systems with constraints.The main job of this paper can be summed up as the following three parts:Firstly,the purpose of this part is to stabilize a class of nonlinear systems with state constraints and control constrains in finite time.First,the model predictive controller is designed to pull system's states into a given area in finite time;in the given area,a Lyapunov-based finite-time controller is constructed to ensure that the system's states can converge to the origin in finite time.During the system is running,the corresponding controllers are switched according to the different states to stabilize the closed-loop system in finite time.Secondly,a finite-time controller based on Lyapunov function is designed for a class of nonlinear systems with constraints and external perturbations,and the estimation of the stability region is given;outside this area,a finite-time optimization controller that it can pull system's states to the stability area in finite time is designed.During the system is running,the corresponding controllers are switched according to the different states to stabilize the closed-loop system in finite time.Thirdly,this part studies the finite-time stability problem of a class of switched nonlinear systems with state constraints and control constrains.For each subsystem,optimization controller is designed by choosing the appropriate Lyapunov function to stabilize the subsystem in finite time,and the estimation of the region of attraction can be prescribed.For the whole switched nonlinear system,a suitable switched law that consist of : 1)at the time of the transition,the value of Lyapunov function wherever the subsystem is reactivated is less than the value of last subsystem's Lyapunov function;2)the switched law can pull state enter the stability region of the mode that the system is switched into is designed to ensure the whole switched nonlinear system can be stable in finite time.