Research On Finite Given Time Control For Nonlinear Systems And Its Application

In the study of control theory, the Lyapunov stability theory has been concerned widely. In practical applications, such as the parafoil systems, missile systems, communications network systems and so on, the general Lyapunov stabilization can not achieve the desired control effect,sometimes it can cause large overshoot due to the external disturbance. Therefore, to study the finite time control is very important, but the settling time depends on the initial state of the system in the existing studies, the finite time control for systems has some limitations. The research on the finite given time control(settling time does not depend on the initial states) has few results. In this paper, the concept of finite given time stability is designed, the finite given time controller for a class of nonlinear systems which is combined with state feedback control and terminal constraint predictive control method is given, and then the presented finite given time controller designed method is applied to the parafoil system trajectory planning optimization problem, the validity of this method is verified.The main results obtained in this paper can be summarized as the following three parts:Firstly, the global finite-given-time stabilization problem is investigated for a class of nonlinear systems. A state feedback control law based on Lyapunov function and a model predictive control law with a terminal region are given. And a suitable switching law is given:when the state of the system is outside the terminal region, the MPC is applied, otherwise the state feedback controller is applied.Secondly, the global finite-given-time stabilization problem is investigated for a class of nonlinear systems with external disturbances. A finite given time state feedback control law and a model predictive control law with a terminal region are given. An appropriate switching rule between the two controllers is designed to guarantee a class of nonlinear systems with external disturbances global finite-given-time stability.Thirdly, the trajectory planning problem of the parafoil system is considered. The finite given time controller for the parafoil systems is designed. Based on the simplification particle motion model of the parafoil systems, the system trajectory optimization problem is converted into a finite given time control problem. The finite given time controller for the parafoil systems is designed, and then the finite given time stability analysis is given. Using the finite given time controller to control the parafoil systems under different initial conditions, we can obtain the trajectory curves.