具有时变统计数字系数的离散时间系统的H2/H无穷控制及其在通信网络中的应用

As one of the most important robust control methods, H2/ H-infinite control has been successfully applied in engineering. The project will generalize the observability and detectability in modern control theory to discrete-time stochastic difference systems with coefficient matrices of time-varying statistics. The design of H2/H-infinite controller is discussed, the inherent relationship among observability, detectability, controller solution and controller gain is revealed, and the conservativeness of stability analysis and the fragility of controller implementation are reduced. On this basis, the developed H2/H-infinite control theory in the system is applied to the communication network control with packet loss, delay and external disturbance. Joint power and rate control algorithms are proposed and the stability analysis framework is established to reveal the effectiveness of the external disturbance, time delay and packet loss on network stability. The research of this project will lay a theoretical foundation for the development and improvement of H2/ H-infinite control of stochastic difference system with the coefficient matrices of time-varying statistics. It can be expected that the theoretical results have great application value in various engineering fields, such as communication network control, etc.

H2/H无穷控制是最为重要的鲁棒控制方法之一,在工程上获得了成功的应用.本项目拟将现代控制理论中的能观性和能检测性推广到具有时变统计数字系数的离散时间随机差分控制系统,讨论这类系统的H2/H无穷控制设计问题,揭示出系统能观性、能检测性、控制器的解和控制器增益的内在关系,降低此类系统稳定性分析的保守性和控制器实现的脆弱性.在此基础上，将所发展的H2/H无穷控制理论成果应用到有丢包、延迟和外部干扰现象的通信网络控制中,建立其功率和流量的联合控制算法及系统稳定性分析框架,揭示出外部干扰、延迟和丢包对网络稳定性的影响.本项目的研究将对具有时变统计数字系数的随机系统H2/H无穷控制的发展和完善奠定理论基础,其理论成果在通信网络控制等其它工程领域中具有很大的应用价值.

本项目研究了H2/H无穷控制及其相关的问题。首先采用分数阶技巧、递归贝叶斯算法和信息融合方法讨论了系统的故障诊断、隔离、估计的技术方案,其次，应用随机分析和计算技巧，提出了具有时变统计数字系数的随机系统的滤波器和控制器的设计方案；应用有限时间命令滤波反步设计方法，提出了几类不确定非线性系统的有限时间控制器方案，最后将有关成果应用于通讯、锂电池、传感器及无人机等工程领域，找到了解决相应问题的行而有效方法和技巧。