时滞正Markov跳变系统的分布式控制与滤波

As modern control systems become more large-scale and complex, distributed control for complex systems is now receiving increasing attention and many practical systems described by positive systems, such as vehicle formation and power systems, arise in research on complex systems. Due to the fact that the theoretical results of general systems can not be directly used for positive systems, and system operation inevitably suffers such constraints as noise, environmental changes and communication failures, this project will investigate the distributed control for continuous-time/discrete-time positive Markov jump systems with time-delays. By taking full advantage of the positivity of systems and applying comprehensively stochastic stability theory, model transformation approach, linear co-positive stochastic Lyapunov functional approach, linear programming approach etc., this project will be developed from the following aspects: it is for the first time to reveal and investigate the positive and negative effects of time-delays on the stochastic stability and system performance of positive Markov jump systems with time-delays; considering the delays in network transmission and the random network topologies caused by communication failures, the complex positive systems will be modeled as positive Markov jump systems with time-delays, and distributed control design will be further considered. This project will enrich and improve theories for positive systems, expedite the original innovation of the control technologies, and promote theoretical and practical values of positive systems in engineering practice.

随着现代控制系统日趋大型化和复杂化，复杂系统的分布式控制研究正迅速兴起，其研究中出现了大量由正系统描述的模型，如车辆编队和电力系统等。由于一般系统的结论不能直接应用于正系统，且系统运行受到噪声、时滞、环境变化、通讯故障等因素的制约，本项目拟研究连续/离散时滞正Markov跳变系统的分布式控制。将充分利用系统的正性，运用随机稳定性理论，以及模型变换、线性余正Lyapunov泛函、线性规划等方法，拟开展：首次研究时滞对正Markov跳变系统的随机稳定性和性能的积极和消极影响；考虑测量时延、数据丢失和噪声等约束，建模Markov随机切换网络拓扑下的复杂时滞正系统，进行分布式控制设计。本项目将丰富和完善正系统的理论体系，形成具有原始创新的控制策略，促进正系统理论在工程中的应用。

现代工业系统中出现了大量正系统描述的模型。由于系统参数的随机跳变特性和信息交互中不可避免的时延特性，时滞正Markov跳变系统的分析和综合引起了关注。本项目主要研究了时滞正Markov跳变系统的随机稳定性和L1/l1 增益性能分析、L1/l1 增益控制与滤波、有限时间随机有界性分析以及有限时间分布式网络化控制与滤波。建立了时滞依赖的随机稳定性和L1/l1 增益性能的充要条件，揭示了时滞对随机稳定性和L1/l1 增益性能的积极与消极作用，并以线性规划条件给出了时滞依赖的L1/l1 增益控制与滤波设计算法。同时，探索了分布式网络化控制系统框架下的基于Markov切换拓扑结构的正系统理论，并提出了时滞依赖的有限时间L1/l1 增益控制方法。..本项目的顺利完成推动了关于正系统、时滞系统和Markov跳变系统的交叉融合研究，丰富和完善了正系统的理论体系，形成了具有原始创新的控制和滤波策略，为时滞正Markov跳变系统理论在工程中的应用提供了理论支撑。