加性噪声下网络化多输入离散系统均方可镇定

Mean square stabilization of multi-input discrete-time systems over additive noise channels

中文关键词  优化序  均方可镇定  加性噪声信道  信道容量  拓扑熵  网络化控制系统

英文关键词  majorization  mean square stabilization  additive noise channels  channel capacity  topology entropy  networked control systems

中文摘要

      本文研究了静态信噪比约束下多输入离散系统均方可镇定问题, 其中信道资源固定且不可任意分配, 信道 被建模为加性高斯白噪声. 主要目的是借用优化序理论讨论系统可镇定时各子信道的信道容量与系统拓扑熵的关 系. 本文基本思想是从供需平衡角度讨论可镇定性. 具体地, 对于通信资源, 每个系统输入被视为需求方, 而信道被 视为供应方. 信道的供应资源由其各自的均方容量刻画, 网络化系统均方可镇定要求通信资源供求平衡. 因信道资 源不可配置, 人们可以通过调节需求方(一定的传输机制)来满足供给方要求. 给出了网络化系统均方可镇定时的一 个充分条件和一个必要条件. 最后数值算例验证所得结论.

英文摘要

      In this paper, the mean square stabilization problem of multi-input discrete-time systems under stationary signal-to-noise ratio (SNR) constraints is studied. The channel resources are fixed and cannot be arbitrarily allocated. The channel is modeled as an additive white Gaussian noise. The main purpose is to discuss the relationship between the channel capacity of each sub-channel and the system topology entropy when the discussed networked control system is stabilized using majorization theory. The basic idea of this paper is to view the stabilization from the perspective of supply and demand balance. Specifically, for communication resources, each system control input is considered as the demand side and the channels are considered as the supply side. The supply resources of the channels are characterized by their respective mean square capacities, and to stabilize the networked system requires the balance of supply and demand of communication resources. Since the channel resources are not configurable, one can satisfy the supplier’s requirements by adjusting the demand side (a certain transmission mechanism). We give a necessary condition and a sufficiency condition for stabilizing the networked control system. Finally, numerical examples verify the conclusions.