Time-varying Formation Analysis Research Articles

Time-Varying Formation Control for Time-Delayed Multi-Agent Systems with General Linear Dynamics and Switching Topologies

Time-varying formation analysis and design problems for general linear multi-agent systems with switching interaction topologies and time-varying delays are studied. Firstly, a consensus-based formation control protocol is constructed using local information of the neighboring agents. An algorithm with three steps is presented to design the proposed formation control protocol. Then, based on linear matrix inequality technique and common Lyapunove–Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with switching topologies and time-varying delays to achieve time-varying formation are given together with a time-varying formation feasibility condition. Finally, a numerical simulation is given to demonstrate the effectiveness of the obtained theoretical results.

Guaranteed-Performance Time-Varying Formation Control for Swarm Systems Subjected to Communication Constraints

Guaranteed-performance time-varying formation analysis and design problems for general high-order swarm systems with communication constraints are investigated. First, a guaranteed-performance time-varying formation control protocol is proposed by using the intermittent relative local information, and the performance function is introduced to guarantee the formation regulation performance among neighboring agents. An explicit presentation of the formation center function is presented to describe the movement trajectory of the formation as a whole. Then, sufficient conditions for guaranteed-performance time-varying formation analysis and design are respectively given by linear matrix inequality techniques, and a guaranteed-performance cost is determined meanwhile. When the desired guaranteed-performance time-varying formation satisfies the time-varying formation feasibility condition, swarm systems with communication constraints can achieve the guaranteed-performance time-varying formation by designing the gain matrix of the guaranteed-performance time-varying formation control protocol if the nominal coverage rate is larger than a positive threshold. Finally, a numerical simulation is shown to illustrate theoretical results.

Time-varying formation control for general linear multi-agent systems with switching directed topologies

Time-varying formation analysis and design problems for multi-agent systems with general linear dynamics and switching directed interaction topologies are investigated. Different from the previous results, the formation in this paper can be defined by specified piecewise continuously differentiable vectors and the switching topologies are directed. Firstly, necessary and sufficient conditions for general linear multi-agent systems with switching directed topologies to achieve time-varying formations are proposed, where a description of the feasible time-varying formation set and approaches to expand the feasible formation set are given. Then an explicit expression of the time-varying formation reference function is derived to describe the macroscopic movement of the whole formation. An approach to assign the motion modes of the formation reference is provided. Moreover, an algorithm consisting of four steps to design the formation protocol is presented. In the case where the given time-varying formation belongs to the feasible formation set, it is proven that by designing the formation protocol using the proposed algorithm, time-varying formation can be achieved by multi-agent systems with general linear dynamics and switching directed topologies if the dwell time is larger than a positive threshold. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.