Distributed optimization for discrete time‐varying linear multi‐agent systems with event‐triggered communication

Abstract This paper studies the distributed optimization problem (DOP) of discrete time‐varying linear multi‐agent systems (MASs), in which the global objective function is formed by a sum of local convex objective functions. Firstly, a DOP with discrete time‐varying MASs is considered, in which the time‐varying linear matrix satisfies a certain equality constraint. To solve this problem, a novel discrete‐time distributed optimization algorithm (DOA) with event‐triggered communication mechanism (ETCM) is proposed. Secondly, by constructing the error dynamical system and using a series of inequality techniques, some sufficient conditions for achieving consensus and obtaining the optimal solution are established. It is found that the considered MAS has generality and the proposed DOA has the advantage of reducing communication burden. Finally, a numerical simulation is presented to verify the validity of theoretical results.