Design of a class of nonlinear consensus protocols for multi‐agent systems

Abstract

SUMMARY This paper investigates the consensus problem for multi‐agent systems and presents a class of nonlinear consensus protocols. First, we reveal some structure property of the corresponding Laplacian matrix by decomposing the interaction graph into strongly connected components. Then, by means of the input‐to‐state stability and algebraic graph theory, we propose a framework to prove consensus for multi‐agent systems with nonlinear protocols. In particular, we prove that consensus can be always reached in systems of single‐integrator agents with a directed communication topology containing a spanning tree, provided the nonlinear protocol is an odd and increasing function. The nonlinear consensus protocols proposed in this paper include the classical linear consensus protocol as a special case, and may have a wide range of applications, including consensus with faster convergence rates and with bounded control inputs. Copyright © 2012 John Wiley & Sons, Ltd.

Design of consensus protocol for nonholonomic systems under directed communication topology

“…Since the directed topology has a spanning tree, m−1 j=1 a mj > 0 and matrix Q 2 is positive definite which has been proved in Theorem 2 in [19]. Hence for the fixed parameter k 1 and nonzero constant δ 3 , the following linear equations have a unique solution:…”

“…where matrix A 1 ii is a scalar or null while A 2 ii is square with dimension at least 2 or null, i = 2, · · · , h. The specific procedure can be referred to in [19]. Actually this form describes the block cascade transmission of the information flow more clearly.…”

Cooperative source localization of multi-agent system based on a cooperative PE condition

“…To get weaker condition on cooperative source localization problem, we will make full and efficient use of the topology information about direct interaction between agents and source which is motivated by [7]. In the Graph G, which consists of one source and N agents, C 1 denotes the set of agents that can directly connect to the source, C 2 denotes the set of the remaining agents that can not directly connect to the source, namely, which can only indirectly obtain the information of the source though agents in C 1 .…”

“…To sum up, our contribution is tripartite: we first figure out what is the direct interaction between agents and the source by graph analysis [7]; instead of the PE condition, a local cooperative estimator is designed to obtain a weaker condition with the aid of the notion of cooperative PE condition; the similar approach is employed to obtain the corresponding result for the case of the dynamic source.…”

Guaranteed cost formation control for multi-agent systems: Consensus approach

“…During the past decades, the distributed cooperative control of multi-agent systems has attached much attention due to their broad applications including formation, flocking, synchronization, rendezvous [1][2][3][4][5][6]. Many researchers focused on formation control problems for a group of agents and many traditional methods were proposed to analysis the formation control for multi-agent systems [7,8], such as leader-follower, behavior, virtual structure, etc.…”