Zhijian Ji

Brief paper: Interconnection topologies for multi-agent coordination under leader-follower framework

In this paper, the formation control problem of the network of multiple agents is studied in terms of controllability, where the network is of the leader-follower structure with some agents taking leaders role and others being followers interconnected via the neighbor-based rule. It is shown that the controllability of a multi-agent system can be uniquely determined by the topology structure of interconnection graph, for which the investigation comes down to that for a multi-agent system with the interconnection graph being connected. Based on these observations, two kinds of uncontrollable interconnection topologies are characterized, and a necessary and sufficient eigenvector-based condition is presented. Our studies also touch upon the selection of leaders.

Controllability of multi-agent systems with time-delay in state and switching topology

In this article, the controllability issue is addressed for an interconnected system of multiple agents. The network associated with the system is of the leader–follower structure with some agents taking leader role and others being followers interconnected via the neighbour-based rule. Sufficient conditions are derived for the controllability of multi-agent systems with time-delay in state, as well as a graph-based uncontrollability topology structure is revealed. Both single and double integrator dynamics are considered. For switching topology, two algebraic necessary and sufficient conditions are derived for the controllability of multi-agent systems. Several examples are also presented to illustrate how to control the system to shape into the desired configurations.

Leaders in multi-agent controllability under consensus algorithm and tree topology ✩

Abstract By controllability of multi-agent systems, we mean the property that all agents can be driven to arbitrary configurations only through regulating a few leaders externally, while the rest of the agents are subject to the nearest-neighbor-law. It is known that the controllability of multi-agent systems depends not only on the communication topologies among agents but also on the selection of leaders. The main objective of this paper aims to characterize the virtue that leaders should have from the perspective of algebraic and graphical conditions. We begin with a heuristic observation for tree graph. To gain more insights, necessary and sufficient conditions are then proposed in terms of downer branch and subgraphs, respectively. In particular, it is shown for path topologies that controllability completely depends on the leaders’ location. The obtained results may help us to pave the way towards a new method of formation and reconfiguration control in swarming robots.

Protocols design and uncontrollable topologies construction for multi-agent networks

This note investigates the controllability issues of multi-agent systems, where each node contains generic linear dynamics. First, a neighbor-based control protocol is proposed, under which it is shown that the controllability of a multi-agent system is solely decided by its communication topology structure. We then further consider the effects of communication topology on the controllability from a graph theory point of view by explicitly constructing topologies. The construction exhibits a partition of the designed graph with identified leaders under which the system is shown to be uncontrollable.

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

This paper addresses robust H ∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level y only by employing state-dependent switching rules. Then the robust H ∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H ∞ -norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

Controllability of multi-agent systems based on agreement protocols

This paper investigates the controllability of multi-agent systems based on agreement protocols. First, for a group of single-integrator agents, the controllability is studied in a unified framework for both networks with leader-following structure and networks with undirected graph. Some new necessary/sufficient conditions for the controllability of networks of single-integrator agents are established. Second, we prove that, under the same topology and same prescribed leaders, a network of high-order dynamic agents is completely controllable if and only if so is a network of single-integrator agents. Third, how the selection of leaders and the coupling weights of graphs affect the controllability is analyzed. Finally, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Decentralized stabilizability of multi-agent systems under fixed and switching topologies☆

Abstract The paper studies decentralized stabilizability for multi-agent systems with general linear dynamics. The stabilizability problem is formulated in a way that the protocol performance can be evaluated by means of the stabilizability region and the feedback gain. For fixed topology, it is proved that the system is stabilizable if and only if external control inputs are exerted on some indicated agents. The result is further shown to be a prerequisite for subsequent design of the corresponding decentralized external self-feedback control, which is also necessary and sufficient. Based on this, two methods are presented to find the agents under which stabilizability can be reached, and the region of stabilizability is given to evaluate the protocol performance. For switching interaction topology, it is shown that the system is stabilizable even if each of its subsystems is not. Finally, the results are employed to cope with the decentralized set-point formation control problem, for which some necessary and/or sufficient conditions are developed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.

Consensus for heterogeneous multi-agent systems under fixed and switching topologies

Abstract The consensus problem for heterogeneous multi-agent systems under directed topologies is investigated. For continuous-time systems, a novel consensus algorithm is proposed. Based on a system transformation method, the consensus problem for heterogeneous multi-agent systems is converted into a consensus problem for homogeneous multi-agent systems. Necessary and sufficient conditions are presented to guarantee that the designed consensus algorithm asymptotically solves the consensus for heterogeneous multi-agent systems under a fixed topology. The final convergence states are shown explicitly for this case. Sufficient conditions are given to guarantee that heterogeneous multi-agent systems reach consensus asymptotically under switching topologies. The obtained results are superior obviously to the existing ones in the literature. The counterparts about discrete-time systems are also investigated. Both periodic sampling and nonperiodic sampling are considered. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

On the controllability of multiple dynamic agents with fixed topology

This paper focuses on the controllability of multi-agent systems with fixed topology based on agreement protocols. We analyze three models of agents: single integrator, double integrator and high-order integrator. For a group of single-integrator agents, controllability is studied in a unified framework for both networks with leader-following structure and networks with undirected graph. Some new necessary/sufficient conditions for controllability of networks of single-integrator agents are established. For networks of double-integrator agents, we prove that controllability of the networks is equivalent to that of networks of single-integrator agents under the same topology and same prescribed leaders. This result is further extended to the case of networks of high-order-integrator agents. Moreover, two influencing factors of controllability of networks are investigated, that is, the selection of leaders and the link weights of graphs.

A graph theory based characterization of controllability for multi-agent systems with fixed topology

The paper studies a class of formation control problem, i.e. the controllability for multi-agent systems under leader-follower framework. A new concept leader-follower connectedness is proposed to deal with what is the desired extent of connectivity between the leader and follower subgraphs for a multi-agent system to be controllable. Analysis based on this concept yields graph theory based characterizations for the controllability of interconnection dynamic networks with fixed topologies.