The guaranteed-performance consensualization for high-order linear and nonlinear multiagent systems with switching topologies is respectively realized in a completely distributed manner in the sense that consensus design criteria are independent of interaction topologies and switching motions. This paper first proposes an adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated. Then, a new translation-adaptive strategy is shown to realize completely distributed guaranteed-performance consensus control and an adaptive guaranteed-performance consensualization criterion is given on the basis of the Riccati inequality. Furthermore, an approach to regulate the consensus control gain and the guaranteed-performance cost is proposed in terms of linear matrix inequalities. Moreover, main conclusions for linear multiagent systems are extended to Lipschitz nonlinear cases. Finally, two numerical examples are provided to demonstrate theoretical results.

Completely Distributed Guaranteed-Performance Consensualization for High-Order Multiagent Systems With Switching Topologies

It is well known that all agents in a multiagent system can asymptotically converge to a common value based on consensus protocols. Besides, the associated convergence rate depends on the magnitude of the smallest nonzero eigenvalue of Laplacian matrix . In this paper, we introduce a superposition system to superpose to the original system and study how to change the convergence rate without destroying the connectivity of undirected communication graphs. And we find the result if the eigenvector of eigenvalue has two identical entries , then the weight and existence of the edge do not affect the magnitude of , which is the argument of this paper. By taking advantage of the inequality of eigenvalues, conditions are derived to achieve the largest convergence rate with the largest delay margin, and, at the same time, the corresponding topology structure is characterized in detail. In addition, a method of constructing invalid algebraic connectivity weights is proposed to keep the convergence rate unchanged. Finally, simulations are given to demonstrate the effectiveness of the results.

/pdf/fast-consensus-seeking-on-networks-with-antagonistic-p9s5axerp2.pdf

Fast Consensus Seeking on Networks with Antagonistic Interactions

In practice, the dual constraints of limited interaction capabilities and system uncertainties make it difficult for large-scale multiagent systems (MASs) to achieve intelligent collaboration with incomplete local relative information. In this article, a review is conducted on the recent development of MASs intended for intelligent control, including consensus problem, formation control, and flocking control. Based on the limitations of the interaction level and the constraints of the individual system level, the published results on intelligent control are categorized into limited sensing-based control, event-based control, pinning-based control, resilient control, and collaborative control under system constraints. Also, the applications of intelligent control for MASs are presented, especially for robotics, complex networks, and transportation. Finally, a discussion is given about the challenges and future directions of research in this field.

A Survey on Intelligent Control for Multiagent Systems

Robust time-varying formation design problems for second-order multi-agent systems subjected to external disturbances are investigated. Firstly, by constructing an extended state observer, the disturbance compensation is estimated, which is a critical term in the proposed robust time-varying formation control protocol. Then, an explicit expression of the formation center function is determined and impacts of disturbance compensations on the formation center function are presented. With the formation feasibility conditions, robust time-varying formation design criteria are derived to determine the gain matrix of the formation control protocol by utilizing the algebraic Riccati equation technique. Furthermore, the tracking performance and the robustness property of multi-agent systems are analyzed. Finally, the numerical simulation is provided to illustrate the effectiveness of theoretical results.

Robust time-varying formation design for multiagent systems with disturbances: Extended-state-observer method

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

Summary
This paper studies the controllability of multiagent systems based on path and cycle graphs. For paths or cycles, sufficient and necessary conditions are presented for determining the locations of leaders under which the controllability can be realized. Specifically, the controllability of a path is shown to be determined by a set generated only from its odd factors, and the controllability of a cycle is determined by whether the distance between 2 leaders belongs to a set generated from its even (odd) factors when the number of its nodes is even (odd). For both graphs, the dimension of the controllable subspace is also derived. Moreover, the technique used in the derivation of the above results is further used to get sufficient and necessary conditions for several different types of graphs generated from path and cycle topologies. These types of graphs can be regarded as typical topologies in the study of multiagent controllability, and accordingly the obtained results have meaningful enlightenment for the research in this field.

Controllability of multiagent systems based on path and cycle graphs

This paper studies the stabilizability and formation control problems of multi-agent systems with antagonistic interactions. The agents run a bipartite consensus protocol using a signed Laplacian which is different from the conventional one. By taking advantage of the proposed structurally balanced independent strongly connected components(SBiSCCs) of the signed graph, a sufficient and necessary condition is presented to solve the decentralized stabilizability problem of multi-agent systems with antagonistic interactions. Besides, formation control is considered and the sufficient and necessary condition is provided by applying the proposed results. Several simulations are given to illustrate the theoretical results.

Decentralized stabilizability and formation control of multi-agent systems with antagonistic interactions.

Stabilizing multiagent systems including unstable agents shows the advantage of cooperation. This paper addresses the problem of stabilization of heterogeneous multiagent systems. Under cycle graphs, a sufficient condition for the stabilization problem via harmonic control is provided and an algorithm of designing the interconnection gains is presented. Furthermore, a sufficient and necessary condition for stabilization problem via harmonic control under cycle graphs is first given when the graph contains less than 5 nodes.

/pdf/stabilization-of-heterogeneous-multiagent-systems-via-1tayi26j77.pdf

Stabilization of Heterogeneous Multiagent Systems via Harmonic Control

For a networked system governed by the consensus algorithm, its controllability can be transformed into the controllability of two kinds of systems. The controllability equivalence of the two systems is proved. Utilizing this property, a novel approach for constructing single-leader controllable networked systems is presented. We also investigate the controllability of a graph when two nodes are added to an original node. Moreover, the controllability of a special class of graph is studied as well.

An approach for constructing single-leader controllable networked systems

This paper studies the controllability problem for weighted digraphs with antagonistic interactions. Based on the graph partition theory, the L-equitable partition(L-EP) is proposed. Using L-equitable partition, a graph-theoretic necessary condition is proposed for the controllability of the multi-agent system and an algorithm is given for the computation of the partition. Besides, the upper bound on the controllable subspace is derived by utilizing the coarsest L-EP under leaders V l when the system is uncontrollable.

Xianzhu Liu

Papers

Controllability of multiagent systems based on path and cycle graphs

Decentralized stabilizability and formation control of multi-agent systems with antagonistic interactions.

Stabilization of Heterogeneous Multiagent Systems via Harmonic Control

An approach for constructing single-leader controllable networked systems

The controllability of weighted and directed networks with antagonistic interactions