奇异摄动Markov跳变时滞系统的多目标鲁棒控制与滤波

As a kind of stochastic delayed systems with complex structure, singular perturbed Markov jump delayed systems can reflect many essential characteristics of stochastic hybrid systems, such as jumping characteristic and singular perturbation characteristic. Therefore, it can more accurately characterize some practical system models. This project is concerned with the multi-objective robust control and filtering problems for singularly perturbed Markov jump delayed systems. Its aims are to establish the available conditions for the existence of admissible controllers/filters and provide the corresponding design methods. Based on the singular perturbed characteristics, the influences of singular perturbation and jumping characteristics on system performance are fully explored. By using the frequency decomposition design method, generalized KYP (Kalman-Yakubovich-Popov) Lemma, stochastic analysis theory, homogeneous design concept and some novel techniques in processing delay-dependent issues, some delay-dependent conditions for the existence of multiple performance criteria, which are less conservative and easy-to-verify, are obtained. With the help of those criteria, the corresponding robust controller/filter design methods satisfying various performance indexes are given, in which the conservativeness and computational complexity are further optimized together. The implementation of this project will further develop and enrich the theory of singular perturbed Markov jump delayed systems, and provide a new reference for the application of such systems in the analysis and control of networked power systems.

奇异摄动Markov跳变时滞系统作为一类具有复杂结构的随机时滞系统，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，故更能准确地表征一些实际系统模型。本项目拟开展奇异摄动Markov跳变时滞系统的多目标鲁棒控制与滤波问题研究，旨在提供行之有效的多目标鲁棒控制器与滤波器的存在条件与设计方法。从奇异摄动特性出发，探求奇异摄动特性和跳变特性对系统性能的影响，利用分频混合设计方法、广义KYP(Kalman-Yakubovich-Popov)引理、随机分析、均一化设计理念以及新奇的时滞处理技术给出一些低保守性、易于验证的多种性能判据并存的时滞相关条件。另外，给出相应的满足多种性能指标的鲁棒控制器/滤波器设计方法，并进一步协同优化所得设计方法的保守性与计算复杂度。本项目的实施，进一步丰富了奇异摄动Markov跳变时滞系统理论体系，并为该系统在电力系统的网络化分析与控制中的应用提供新的依据。

作为一类既可反映随机混杂系统的跳变特性也能刻画系统多时间尺度特性的系统，奇异摄动Markov跳变系统近年来已成为控制科学与工程研究的热点之一。本项目针对几类具有复杂结构的奇异摄动Markov跳变系统，分别从不完整转移概率问题、时滞问题和非线性特性出发，研究了其多目标鲁棒控制与滤波问题，给出了行之有效的多目标鲁棒控制器与滤波器的存在条件与设计方法。项目组首先从奇异摄动切换系统的确定性时间切换机制入手，深入到复杂的Markov随机切换机制，由浅及深，重点分析和考虑了不完整转移概率和奇异摄动特性对系统性能的影响。基于新颖的时滞相关分析法、随机分析、均一化设计理念以及矩阵解耦技术给出了一些低保守性、易于验证的多种性能判据并存的条件，并在进一步协同优化所得设计方法的保守性与计算复杂度的基础上，给出相应的满足多种性能指标的鲁棒控制器/滤波器设计方法。本项目是研究奇异摄动Markov跳变系统的前沿课题，进一步丰富了该类系统的理论体系，并为该类系统的应用提供新的依据。