Guaranteed Consensus Control of Mobile Sensor Networks With Partially Unknown Switching Probabilities
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摘要: 本文研究了基于马尔科夫切换拓扑的移动传感网保性能一致性问题.网络拓扑切换由一般的马尔科夫链驱动,其初始和转移概率部分未知.切换拓扑集中的每个拓扑皆是带有树的有向拓扑图.借助定义包括接收、发送信息和控制输入的新的全局能耗函数,可以得到切换分布式一致性控制器集合.然后经过状态变换,一致性控制问题转化为减阶的马尔科夫跳跃系统的保性能问题.通过分析马尔科夫跳跃系统的稳定性,提出了可以同时计算次优的一致性控制器增益和次小能耗上界的算法.最后,通过数值仿真检验了控制器设计方法的性能.Abstract: This paper studies the guaranteed consensus of mobile sensor networks (MSNs) with stochastic switching topologies. The switching of topology is triggered by a Markov chain, whose initial and transition probabilities are partially unknown. Each topology in the switching topology set is a directed graph with a spanning tree. A set of distributed switching consensus controllers are derived by means of stability analysis of Markovian jump systems. This is achieved by defining a novel topology-aware cost function of the MSNs involving cost consumption for information receiving, sending and control. By state transformation, the initial dynamics of MSN is reduced to a Markovian jump system with guaranteed cost. A computational algorithm is proposed to simultaneously calculate both the sub-optimal controller gains and the sub-minimal upper cost bound. Eventually, the performance of the controller design method is verified by numerical examples.
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Key words:
- Mobile sensor networks (MSNs) /
- Markov switching topologies /
- mean-square consensus /
- guaranteed cost control
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Fig. 4 Positions of the nodes in the MSN with controller design method in [30].
Algorithm 1. Step 1: Set the initial state $x_i (0)$ $(i=1, {\ldots}, N)$ , weight matrices $Q1, Q2$ , $R$ and the computational accuracy $\varepsilon $ . Let $e=0$ . Step 2: Find a feasible solution $\bar {\delta }$ of $\delta $ by solving (38), set $f=\bar {\delta }$ . Step 3: Let g=(e+f)/2, $\delta =g$ . Solving (38), if there exist feasible the solutions $K_l $ ( $l\in S)$ , set $f=g$ . Otherwise, $e=g$ . Step 4: If $\left| {e-f} \right|<\varepsilon $ , output $\delta $ and $K_l $ . Otherwise, go to Step 3. -
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