随机乘性噪声约束下多输出离散系统均方可检测性

Mean square detectability of multi–output discrete–time systems over stochastic multiplicative noise channels

中文关键词  离散时间控制系统  信道容量  均方可检测  控制不等式  乘性噪声

英文关键词  Discrete time control systems  channel capacity  mean square detectability  majorization  multiplicative noise

中文摘要

      本文主要讨论乘性噪声约束下, 多输出离散系统均方可检测问题. 假定子信道容量是先验固定的, 不能任 意分配. 首先, 利用乘性噪声对通信信道进行建模, 基于编码/观测器协同设计思想, 建立系统均方可检测动态方程. 其次, 根据控制不等式性质和能控性分解技术, 给出网络化系统可检测的充分条件. 再次, 基于循环分解技术, 系统 最优补灵敏度以及控制不等式理论等, 求得网络化系统可检测的必要条件. 所给出的充分和必要条件可用开环系统 拓扑熵与子信道信道容量以控制不等式形式表示. 最后, 数值算例及仿真验证结论的合理性.

英文摘要

      This study discusses the detectability of multiple output discrete-time systems under multiplicative noise constraints. It is assumed that the capacities of sub-channels are fixed prior and cannot be arbitrarily allocated. First, a multiplicative noise is used to model the communication channel, and the dynamic equation of the systems is established by virtue of the coding/observer co-design idea. Second, according to the properties of majorization and controllable decomposition technique, a sufficient condition for the detectability of the networked control systems (NCSs) is given. Meanwhile, based on the cyclic decomposition technique, the optimal complementary sensitivity and the majorization theory, a necessary condition for the detectability of the NCSs is also obtained. The sufficient and necessary conditions can be expressed by the form of majorization, which is composed of the topology entropy of the open loop system and the channel capacities of sub-channels. Finally, the rationality of the conclusion is verified by numerical examples and simulation