Consensus analysis of hybrid multiagent systems: A game‐theoretic approach

Abstract

Summary This paper considers a consensus problem for hybrid multiagent systems, which comprise two groups of agents: a group of continuous‐time dynamic agents and a group of discrete‐time dynamic agents. Firstly, a game‐theoretic approach is adopted to model the interactions between the two groups of agents. To achieve consensus for the considered hybrid multiagent systems, the cost functions are designed. Moreover, it is shown that the designed game admits a unique Nash equilibrium. Secondly, sufficient/necessary conditions of solving consensus are established. Thirdly, we find that the convergence speed of the system depends on the game. By the mechanism design of the game, the convergence speed is increased. Finally, simulation examples are given to validate the effectiveness of the theoretical results.

Scaled consensus for asynchronous high‐order discrete‐time multiagent systems

“…Proof. According to (13), we can obtain that matrix I n ⊗ Λ(t k ) − (t k ) ⊗ Φ(t k ) is nonnegative and contains positive diagonal elements, which together with the fact that the matrix 1…”

“…In Lemma 2, we have obtained a sufficient condition to guarantee the nonnegativity of coefficient matrices Ξ(t k ), k ∈ N, which is in terms of some given constants g i,min , i = 1, 2, … , p that satisfy condition (13). Then, according to condition (9), we can design the following parameters selection strategy:…”

“…According to (15), we can always find appropriate gain parameters 1 , 2 , … , p−1 to guarantee the nonnegativity of the coefficient matrices Ξ(t k ), k ∈ N in system (11) for any given constants g i,min , i = 1, 2, … , p that satisfy condition (13).…”

“…In order to realize consensus, a suitable distributed control protocol needs to be designed to ensure that all agents converge to a common point or state value asymptotically over time. Based on matrix theory, graph theory, Lyapunov functions, and other effective tools, the consensus problems for a team of agents with first‐order or second‐order dynamics have been deeply studied in the literature …”

“…Based on matrix theory, graph theory, Lyapunov functions, and other effective tools, the consensus problems for a team of agents with first-order or second-order dynamics have been deeply studied in the literature. [7][8][9][10][11][12][13] Recently, many new consensus problems have emerged, such as group consensus [14][15][16][17][18] and scaled consensus, [19][20][21][22][23] etc. In the problem of scaled consensus, which was proposed by Roy, 19 each agent has a unique scale that is independent of other agents'.…”