基于Markov跳变概率不确定模型的带宽受限网络控制系统有限时间控制

Aiming at the scientific problem of the control performance degradation or even unstability in finite time induced by the limited bandwidth of networked control systems, the Markov unified model, the selection mechanism for Markovian uncertain transition probabilities, and the finite time control method for networked control systems with limited bandwidth are focused in this project. The discrete, bounded Markov chain is applied to depict the dynamic and random characteristics of the limited bandwidth, and two mutual dependent Markov chains are adopted to describe the coupling of limited bandwidths in both forward and backward communication links. The specific modes are employed to describe the data transmission delays and packet losses induced by the limited bandwidth. Then the unified Markov model for networked control systems with limited bandwidth is constructed. The selection mechanism for Markovian uncertain transition probabilities is studied by combining with Markovian jump linear systems theory and robust uncertainty control theory, and the internal relationship between the Markovian uncertain transition probabilities and the closed-loop system performance is revealed. By the expanding H-Representation method and considering the dynamic performance, the stability analysis and controller designed in finite time are studied, and the conditions for the stability and stabilization are achieved for networked control systems with limited bandwidth. The achievements of the project are expected to enrich the modeling methodology, reveal the mechanism for Markovian uncertain transition probabilities, and provide a theoretical basis for realizing the finite time control of networked control systems with limited bandwidth.

针对带宽受限导致网络控制系统在有限时间内控制性能下降与失稳问题，本项目开展带宽受限网络控制系统的Markov统一模型、Markov跳变概率不确定对系统性能的影响机制、有限时间控制方法三方面研究。采用离散有限模态Markov链刻画动态随机受限带宽，通过Markov链嵌套解耦前向/反馈通道受限带宽耦合，采用Markov特定模态描述受限带宽衍生的时延及丢包，建立带宽受限网络控制系统Markov统一模型；结合Markov跳变线性系统论及鲁棒不确定论，探索概率不确定机理，揭示跳变概率不确定影响带宽受限网络控制系统性能本质；通过推广H-Representation方法，兼顾系统动态性能，研究带宽受限网络控制系统有限时间内稳定性及镇定控制器设计，获得系统随机稳定及镇定判据。研究结果将为带宽受限网络控制系统建模提供新思路，为跳变概率选取机制提供理论依据，为实现带宽受限网络控制系统有限时间控制提供研究基础。

随着计算机网络广泛应用和控制技术不断发展，越来越多闭环反馈控制应用将基于网络环境运行。网络化控制代替传统的点对点控制方式，使得信息资源得到共享，减少了系统布线，易于系统诊断和维护，提高了系统的可靠性和灵活性。然而，受限带宽的引入使得网络控制系统面临着稳定性和能效性两方面的设计要求，给系统的建模、稳定性分析及镇定控制器设计带来更大挑战。针对带宽受限导致网络控制系统在有限时间内控制性能下降与失稳问题，本项目开展了带宽受限网络控制系统的Markov统一模型、Markov跳变概率不确定对系统性能的影响机制、鲁棒控制方法三方面研究。采用离散有限模态Markov链刻画动态随机受限带宽，通过Markov链嵌套解耦前向/反馈通道受限带宽耦合，采用Markov特定模态描述受限带宽衍生的时延及丢包，建立带宽受限网络控制系统Markov统一模型；结合Markov跳变线性系统论及鲁棒不确定论，探索概率不确定机理，揭示跳变概率不确定影响带宽受限网络控制系统性能本质；通过推广H-Representation方法，兼顾系统动态性能，研究带宽受限网络控制系统有限时间内稳定性及镇定控制器设计，获得系统随机稳定及镇定判据。本项目通过揭示带宽受限机理，建立带宽受限网络控制系统的Markov统一模型，通过阐明Markov跳变概率不确定规律，揭示跳变概率不确定对带宽受限网络控制系统性能的影响机制，通过推广H表示方法，为实现带宽受限网络控制系统鲁棒随机稳定及镇定提供研究基础。