Distributed Multi-Target Rotating Encirclement Control of Second-Order Multi-Agent Systems With Nonconvex Input Constraints

This paper investigates the collective multi-target rotating encirclement formation problem of second-order multi-agent systems, where the inputs are constrained in nonconvex sets. The objective requires that all agents rotate around targets' geometric center with the desired radius and angular velocity. Firstly, the targets' geometric center and rotating radius are calculated by two distributed fixed-time estimators based on the neighbors' information. Then, with the complex domain theory, we construct two consensus vectors complying with the conditions of the multi-target rotating encirclement formation, and propose a distributed multi-target rotating encirclement control scheme to force all agents achieve the desired formation structure. Moreover, a sufficient condition is provided for choosing design parameters with the aid of Lyapunov theory. In order to handle the problem caused by the nonconvex input constraints, a constraint operator is introduced to ensure all control inputs always lie in the corresponding nonconvex sets. Finally, numerical simulation results are presented to demonstrate the effectiveness and correctness of our theoretical control scheme.