非线性奇异系统的鲁棒控制

This project systemically studied the problems of tracking control, feedback control, robust regularization, robust tracking and robust stabilization, etc., for certain and/or uncertain nonlinear singular systems, by means of differential geometries method and algebraic analysis method. Based on regularization algorithm, the conditions for standardability of nonlinear singular systems are presented. By using the decoupling method, the regularable nonlinear singular system is transformed into a canonical mode. The stabilized feedback controls are constructed by backstepping method. The output feedback tracking controllers are designed to make the closed- loop system not include the impulse mode and the output track the given reference signal. A kind of similar composite singular systems is dealt with. The decentralized robust station feedback controllers with similar structure are designed by Lyapunov method. At the same time, some control problems on electrical power systems are studied by means of nonlinear backstepping method in singular systems. The research works and research results provide the principles and methods for the feedback design of nonlinear singular systems.

本课题以非线性奇异系统为对象，采用代数分析方法，研究此类系统的跟踪控制、反馈控制、鲁棒正则化、鲁棒跟踪及鲁棒镇定等问题。由于绝大多数实际系统存在高度非线性性及状态间或状态与控制间的等式约束，需要用非线性奇异系统来描述，而且此领域中存在许多有待解决的问题。所以研究非线性奇异系统的鲁棒控制有着重要理论价值和广泛实际意义。..