切换信号受限的切换系统的稳定性及控制设计

This project will study analysis and design issues for switched systems with constrained switching signals. The focus will be put on constraints of neighbor-type and performance induced –type. In the analysis aspect, we will establish constraint-dependent stability criteria for arbitrary switchings subject to the constraints, and the method of multiple Lyapunov functions for constrained switching signals. We will study how the topological structures of the neighbors influence the system behaviors. We will present performance-dependent stability conditions for switched systems with performance-induced constraints on switching signals. For design issues, we will establish co-design methods of controllers and switching laws in presence of constrains on switching signals, especially for basic design problems such as stabilization using the method of multiple Lyapunov functions subject to the constraints. In addition, we will study potential applications, mainly in switching control design for aero-engines.. The results of the study will help discover the interaction between continuous dynamics and discrete dynamics and the function of constrains of switching signals. The study will establish systematic analysis and design methods for switched systems with typical constrained switching signals. The results will provide possible methods and ideas to solve constrained problems of practical systems.

本项目研究切换信号受限的切换系统的分析和设计问题。主要针对邻域型约束和性能诱导型约束进行研究。在分析方面, 我们要建立与约束条件相关的满足受限情形下的任意切换的稳定性的判据；建立在切换信号受限范围内的多Lyapunov函数方法；研究邻域型约束的拓扑结构对于系统性能的影响；获取性能依赖的受限切换系统的稳定性判据。在设计方面，提出切换信号受限情况下的切换律与控制器的联合设计方法，特别是使用受限情形下的多Lyapunov函数方法，解决切换信号受限的切换系统的镇定等基本控制问题。另外，还将研究可能的应用，主要是在航空发动机切换控制设计方面的应用。. 项目的研究将揭示连续动态，离散动态之间的相互作用规律以及切换信号受限在其中的作用；建立典型切换信号受限情形下的系统的分析和设计方法；并为解决实际系统中的受限问题提供可能的方法和思路。

本项目研究了切换信号受限的切换系统的分析和设计问题。主要针对邻域型约束和性能诱导型约束进行研究。在分析方面, 建立了与约束条件相关的满足受限情形下任意切换的稳定性判据；提出了在切换信号受限范围内的多Lyapunov函数方法；揭示了邻域型约束的拓扑结构对于系统性能的影响；得到了性能依赖的受限切换系统的稳定性判据。在设计方面，提出了切换信号受限情况下的切换律与控制器联合设计方法，特别是使用受限情形下多Lyapunov函数方法，解决了切换信号受限的切换系统镇定等基本控制问题。另外，针对航空发动机多目标切换控制设计问题，提出了各种设计方法。项目的研究揭示了切换信号受限情况下离散切换律、系统连续动态和控制器之间的耦合作用，建立了在切换信号受限情况下切换系统稳定性理论分析框架， 统性地提出了控制器和切换律协同设计方法，完善和发展了非线性切换系统的设计理论。