Zhenwei Liu

State synchronization of homogeneous continuous-time multi-agent systems with time-varying communication topology in presence of input delay

This paper studies state synchronization of homogeneous continuous-time multi-agent systems (MAS) with time-varying communication topology in the presence of time-varying input delay. An upper bound for delay tolerance is obtained via a Lyapunov-Krasovskii functional-based method. This upper bound for the delay only depends on the agent dynamics and some rough information about the Laplacian matrix associated with the time-varying communication topology. For any delay satisfying this upper bound, a purely decentralized protocol based on a low-gain methodology is designed for each agent such that synchronization can be achieved without detailed knowledge about the network.

Passivity based state synchronization of homogeneous discrete-time multi-agent systems via static protocol in the presence of input delay

This paper studies state synchronization of homogeneous discrete-time multi-agent systems (MAS) with partial-state coupling (i.e., agents are coupled through part of their states) via static protocol in presence of input delay. Both uniform input delay and nonuniform input delay are considered. We identify one class of agents for which static linear protocol can be designed, which is named squared-down passifiable via input feedforward. A parameterized static protocol is proposed for each agent such that state synchronization is achieved among agents with uniform or nonuniform input delay. Moreover, we derive upper bounds for uniform and nonuniform input delay that can be tolerated.

Solvability conditions and design for H∞ & H2 almost state synchronization of homogeneous multi-agent systems

Abstract This paper studies the H∞ and H2 almost state synchronization problem for homogeneous multi-agent systems with general linear agents affected by external disturbances and with a directed communication topology. Agents are connected via diffusive full-state coupling or diffusive partial-state coupling. A necessary and sufficient condition is developed for the solvability of the H∞ and H2 almost state synchronization problem. Moreover, a family of protocols based on either an algebraic Riccati equation (ARE) method or a directed eigen structure assignment method are developed such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H∞ and H2 norm of the corresponding closed-loop transfer function, is reduced to any arbitrarily small value. The protocol for full-state coupling is static, while for partial-state coupling it is dynamic.

State synchronization of multi-agent systems via static or adaptive nonlinear dynamic protocols

This paper studies state synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling (i.e., agents are coupled through part of states). We identify three classes of agents, for which static linear protocols can be designed. They are agent which are squared-down passive, squared-down passifiable via output feedback, or G-minimum-phase with relative degree 1. We find that, for squared-down passive agents, the static protocol does not need any network information, as long as the network graph contains a directed spanning tree, while for the other two classes of agents, the static protocol needs rough information on the network graph, in particular, a lower bound of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. However, when adaptive nonlinear dynamic protocols are utilized, even this rough information about the network is no longer needed for the other two classes of agents.

Solvability condition for synchronization of discrete-time multi-agent systems and design

This paper provides solvability conditions for state synchronization with homogeneous discrete-time multi-agent systems (MAS) with a directed and weighted communication network under full-state coupling. We assume only a lower bound for the second eigenvalue of the Laplacian matrices associated with the communication network is known. For the rest the weighted, directed graph is completely arbitrary. Our solvability conditions reveal that the synchronization problem is solvable for any nonzero lower bound if and only if the agents are at most weakly unstable (i.e., agents have all eigenvalues in the closed unit disc). However for a given lower bound, we can achieve synchronization for a class of unstable agents. We provide protocol design for at most weakly unstable agents based on either a direct eigenstructure assignment method or a standard H2 discrete-time algebraic Riccati equation (DARE). We also provide a protocol design for strictly unstable agents based on the standard H2 DARE.

Solvability conditions and design for state synchronization of multi-agent systems

This paper derives conditions on the agents for the existence of a protocol which achieves synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling, where the communication network is directed and weighted. These solvability conditions are necessary and sufficient for single input agents and sufficient for multi input agents. The solvability conditions reveal that the synchronization problem is primarily solvable for two classes of agents. This first class consists of at most weakly unstable agents (i.e. agents have all eigenvalues in the closed left half plane) and the second class consists of at most weakly non-minimum-phase agents (i.e. agents have all zeros in the closed left half plane). Under our solvability condition, we provide in this paper a design, utilizing H ∞ optimal control technique.