滑模与适定运动统一的稳定条件及基于值函数的受约束切换系统控制研究

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，针对受约束切换系统采用值函数构建控制器族，研究基于值函数的受约束切换系统空间解耦控制器设计方法。切换系统轨迹在穿越切换面时的运动在一定条件下可以表现为滑模运动或适定运动，通过本项目研究将滑模运动和适定运动稳定性条件统一在一起，同时构建控制器设计的空间解耦条件、构造可切换集，使得约束子系统的控制可以单独设计，构成完整的闭环切换系统。值函数是根据动态规划原理采用反曲变换有限差分数值算法求解后退时域控制框架下的优化问题而得到，并根据值函数、广义速度和控制量之间的关系，给出滑模运动和适定运动统一稳定性条件、反馈滑模化的充分条件及本征滑模面方程，如果切换系统在切换超平面发生滑模运动，滑模到达条件不再是闭环系统稳定的必须条件。闭环系统是全局稳定或半全局稳定的，控制器是实时的可工程实现的。

This project aims to research topics at the forefront of the control theory. Under the framework of the solution to the optimal control problem, the value-function-based space-decoupling controller is designed for the constrained switched system. The motion of the switched system crossing the switching hyperplane could be the sliding-mode motion or the well-posed motion under different conditions. The stability conditions for the sliding-mode motion and the well-posed motion are unified according to the research of this project. The space decoupling conditions, the switchable set for the controller design are constructed. Those conditions make the controller design of the constrained subsystems be done alone to form the whole closed-loop system. The controllers of the constrained subsystems are designed based on the value function. The value function is obtained by solved the optimal control problem arising in the receding horizon/robust receding horizon control schemes using the finite difference approximation with sigmoidal transform (FDAST) algorithm. According to the relationship between the gradient field of the value function, the generalized velocity field and the value of control, the unified stability conditions, feedback-sliding-motionized conditions and the essential sliding-mode surface’s equation are given. If the sliding-mode motion happens on the switching hyperplane under some conditions, the reaching conditions are not necessary in this controller design framework. The whole closed-loop switched system is globally or semi-globally stable. The controller is real-time and can be implemented in engineering