Time-Varying Formation Control For Second-Order Discrete-Time Multi-Agent Systems With Switching Topologies and Nonuniform Communication Delays

Time-varying formation control and velocity tracking problems for second-order discrete-time multi-agent systems with switching jointly-connected topologies and nonuniform communication delays are investigated. A local information-based distributed protocol is designed by utilizing the instantaneous states of the agent itself and the delayed states of its neighbors. Through model transformation and stability analysis, an explicit mathematical description of a feasible time-varying formation set is proposed. Necessary and sufficient conditions for the systems with switching topologies and nonuniform communication delays to achieve the feasible time-varying formation are obtained. The coupling constraints on the gain parameters and sampling period are proposed, so as to guide the design of parameters in the protocol. We include the effects of velocity tracking error damping gain in the protocol and derive milder conditions which allow for not only bounded nonuniform communication delays but also for dynamically switching directed graphs that are jointly connected. The numerical examples are further presented to illustrate the validity and effectiveness of the obtained results.