非线性系统优化控制的数值解法统一框架及滑模后退时域控制算法研究

本项目旨在研究目前控制理论中的前沿课题，在优化控制问题求解的框架下，将滑模控制与后退时域控制统一在一起，研究确定性的及带有未建模动态的非线性系统的滑模后退时域控制算法。根据动态规划原理，采用带有反曲变换的有限差分数值算法求解滑模后退时域控制中的优化控制问题，用求得的值函数确定滑模面并作为控制器设计参数，根据逆李亚普诺夫方法，进行滑模后退时域控制器设计，所求得的控制器既是滑模控制器也是后退时域控制器，这样就将滑模控制及后退时域控制统一在一起。在确保全局稳定或半全局稳定的条件下，所提算法的显著特点是:(1)滑模面的确定不再由人为选取，而是由值函数决定，滑模到达条件不再是必须的，简化了滑模控制设计理论;(2)不依赖于目前后退时域控制算法研究中优化问题在初始点的可解性隐含假设;(3)将确定性和不确定性非线性系统的优化控制问题采用统一的格式求解;(4)控制器的实现是实时的;使得研究的控制器可工程实现

This project aims to research topics at the forefront of the control theory.Under the framework of the solution to the optimal control problem, sliding mode control schemes and receding horizon control schemes are unified together. We research sliding mode receding horizon control schemes for certain and uncertain nonlinear systems.According to the principle of dynamic programming, the finite difference approximation with sigmoidal transform (FDAST) algorithm is proposed to solve the optimal control problem arising in the sliding mode receding horzon control schemes.Then, according to the inverse Lyapunov method, the obtained value function is used to decide the sliding mode plane and also used as the controller design parameter to design the sliding mode receding horizon controller of nonlinear systems. Thus, obtained controllers are both sliding mode controllers and receding horizon controllers. In this way, sliding mode control scheme and receding horizon control scheme are unified together.Under the condition to ensure global stability or semi-global stability, the proposed method has the following features. Firstly, the sliding mode plane is no longer selected by the designer, but it is decided by the value funtion. The stable region is global or semi-global. Sliding mode reaching condition is no longer necessary, thus simplify the design of sliding mode control of nonlinear system. Secondly, the closed-loop system stability does not depend on the implicit assumption in the feasibility of the initial point in receding horizon control schemes. Thirdly, the optimal control problem of certainty and uncertaint nonlinear systems is solved in a unified format. Finally, the implemented controller is real-time. Because of above features, the studied control scheme can be implemented in engineering practice.