Guaranteed cost consensus for second-order multi-agent networks with time-varying delays and cost constraints

Abstract

This article investigates the current guaranteed cost consensus control for multi-agent networks with time-varying delays and cost constraints. First, a guaranteed cost consensus control protocol with a linear quadratic function is proposed to make a tradeoff decision between the consensus regulation performance and control cost consumption. Then, for the case without a cost constraint, the main theorem provides sufficient conditions to reach the leader-following guaranteed cost consensus with switching transmission topologies, where the time-varying delay term is handled using the derivative form. The upper bound for the linear quadratic function is calculated; it is related to the time-varying delays and the initial conditions. Moreover, guaranteed cost consensus analysis criteria are developed for the case including a cost constraint. The correlation between the cost constraint condition and an explicit guaranteed cost upper bound is constructed, and the matrix dimension is independent of the number of agents. Finally, the obtained theoretical results are verified through numerical simulations.