Average consensus with weighting matrix design for quantized communication on directed switching graphs

Abstract

We study average consensus for directed graphs with quantized communication under fixed and switching topologies. In the presence of quantization errors, conventional consensus algorithms fail to converge and may suffer from an unbounded asymptotic mean square error. We develop robust consensus algorithms to reduce the effect of quantization. Specifically, we introduce a robust weighting matrix design and use the H 1 performance index to measure the sensitivity from the quantization error to the consensus deviation. Linear matrix inequalities are used as design tools. The mean square deviation is proven to converge and its upper bound is explicitly given in the case of fixed topology with probabilistic quantization. Numerical results demonstrate the effectiveness of this method. 520 S. LI ET AL.in a practical network. The authors in [13] consider the continuous-time quantized consensus problem, where a discontinuous protocol is designed to restrict the dynamic evolving towards the initial average. However, there exists unavoidable chattering in practice, and replacing the discontinuous function with a hysteresis, one remedies the problem but reduces accuracy. A protocol featuring an attractive property of preserving the initial average throughout the iterations was proposed in [14]. This protocol drives the system close to the average consensus with a bounded error. To further reduce the quantization error effects, a sequence averaging algorithm based on this sum-preserving protocol was proposed in [15]. Meanwhile, [16][17][18] studied the quantization problem in gossip based consensus algorithms. In [18], the author proposed two different protocols, that is, a globally quantized strategy and a partially quantized strategy, respectively. For the globally quantized strategy, it was shown that all states eventually reach agreement, but the value of the agreement is different from the initial average. In contrast, the partially quantized strategy preserves the average and the consensus error is bounded by one (states are quantized to integers) after a finite period of time. The partially quantized strategy is also studied in [16,17] and similar conclusions are extended to general quantizers. It was shown that the consensus error of this algorithm is bounded by one but whether or not the consensus error can be further reduced was not explored.In this paper, we consider distributed consensus on directed switching communication graphs, which are used to model many real communication systems [19]. Specifically, inspired by the idea of robust H 1 consensus control [20], we model the problem as a robust consensus design problem with mismatched quantization noises and design the weighting matrix of the average consensus protocol introduced in [14] under the H 1 performance index to mitigate the consensus deviation caused by quantization errors. Using linear matrix inequality (LMI) as design tools, we show that the consensus deviation is bounded by a pre-designated constant. For a probabilistic quantization scheme on direct...

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“…Corresponding applications to cooperative multi-robot systems were reported in [30,31]. An alternative solution to address this issue was reported in [32], where common Lyapunov functions are defined for the average consensus problem with weighting matrix design, for quantized communication on directed switching graphs.In order to overcome the problems emerging from non-homogeneity and unreliable communication links, this paper proposes adaptive consensus strategies for cooperative MAS subjected to dynamic network topologies and evolving in unfamiliar, unstructured and dynamic environments. Our research is motivated by search and rescue tactics during disaster response, where the detection and tracking of multiple assets (e.g.…”

“…Corresponding applications to cooperative multi-robot systems were reported in [30,31]. An alternative solution to address this issue was reported in [32], where common Lyapunov functions are defined for the average consensus problem with weighting matrix design, for quantized communication on directed switching graphs.…”