Network sensitivity function, optimization and robust performance in dynamic average consensus

Abstract

AbstractIn this article, a novel sensitivity minimization approach is proposed to optimize the performance of proportional‐integral (PI) dynamic average consensus (DAC) algorithms subject to measurement noises and model uncertainties. Network sensitivity and complementary sensitivity functions are defined to characterize the effects of the reference signals and measurement noises on the tracking error, respectively. Minimization of the norms of network sensitivity and complementary sensitivity functions, describing how large the PI DAC algorithm amplifies the reference and noise signals in the worst case, are conducted to optimize the tracking performance with respect to the reference signals and measurement noises without requiring prior knowledge. Further, by studying the weighted optimization of the network sensitivity functions, necessary and sufficient conditions are provided for the PI DAC algorithm to have a good tracking performance for low‐frequency reference signals and high‐frequency measurement noises. The proposed sensitivity minimization approach is shown to be a robust approach, by considering the PI DAC algorithm in the presence of norm‐bounded additive uncertainties. The robust weighted performance specification is formulated and a sufficient condition is provided, relying on the network topology, the bound of the uncertainties, and the parameters of the DAC algorithms. A tradeoff relationship between the tracking performance and robustness is unveiled. The special case of proportional DAC algorithms is similarly discussed.