基于双层模态的奇异摄动随机跳跃系统分析与控制

Singularly perturbed stochastic jumping systems are a kind of system models with strong application background, which can reflect the two-time scale property of the singularly perturbed systems, the stochastic jumping characteristics and many other structural features. In this project, for the singularly perturbed stochastic jumping systems with two-layer modes, the robustness analysis and control synthesis problems are addressed by considering the key factors, such as system structure, limited network dynamic characteristics and system performance. The purpose of this project is to explore the influence of information acquisition, the analysis of singular perturbation parameter, the limitation of network dynamic characteristics and the nonlinear structure on the analysis and control problems of singularly perturbed stochastic jumping systems. Based on the two-layer modes structure concept, fuzzy fast/slow dynamic decomposition strategy, the round robin scheduling scheme, persistent dwell time switching technology, convex optimization technique and stochastic process analysis theory, the singularly perturbed stochastic jumping systems with two-layer modes are analyzed deeply. Some performance analysis methods are explored and the corresponding control design strategies which can be easily realized and take the control effect into account are presented. In summary, this project will not only enrich the control theory of singularly perturbed stochastic jumping systems to some extent, but also underpin their applications in the modeling and control of wind power systems.

奇异摄动随机跳跃系统是一种具有很强应用背景的系统模型，能反映出奇异摄动系统的双时间尺度特性与系统随机跳跃特性等诸多结构特征。本项目以基于双层模态的奇异摄动随机跳跃系统为对象，从系统结构、网络以及性能等重要因素出发，研究该类系统的鲁棒分析与控制综合问题。旨在探究模态信息获取与奇异摄动参数分析、网络动态特性受限以及非线性结构对奇异摄动随机跳跃系统分析与控制设计的影响。拟通过双层模态结构概念、模糊快慢动态分解策略、轮询调度策略、持续驻留时间切换技术、凸优化技术以及随机过程分析理论，深入剖析基于双层模态的奇异摄动随机跳跃系统的特殊结构，探索奇异摄动随机跳跃系统的性能分析方法，萃取出更容易实现且能顾及到控制效果的控制综合设计策略。从而，在一定程度上丰富奇异摄动随机跳跃系统的控制理论体系，为此类系统在风力发电网络的建模与控制中的应用提供新的支撑。

奇异摄动随机跳跃系统作为一类具有复杂结构的随机系统，能反映出随机混杂系统的跳变特性和奇异摄动特性等许多本质特征，故能更准确地表征一些实际系统。本项目开展了具有双层模态下奇异摄动跳跃系统的分析与控制问题研究。从奇异摄动特性出发，探求了奇异摄动特性和双层模态特性对系统性能的影响，利用随机稳定性理论、半Markov核方法、随机分析以及新颖的矩阵解耦技术给出了一些低保守性的多种性能判据条件，提出了行之有效的切换控制器与观测器设计方法，并协同优化了奇异摄动参数。本项目的实施进一步丰富了奇异摄动随机跳跃系统理论体系，并为实际应用提供新的技术支撑。