Theory and Experiment of Enclosing Control for Second-Order Multi-Agent Systems

This article investigates the enclosing control without preset formation of second-order multi-agent systems for stationary targets. This article uses a directed graph to describe and the direction of information exchange between agents and targets. For continuous-time systems, an enclosing control algorithm is proposed, which does not need to preset the desired formation. The state transfer equation is used to transform the solution of the system into a matrix function of first-order linear constant-coefficient non-homogeneous differential equations. By analyzing the convergence of the solution, the value range of the gain parameter is obtained, and the requirements of topology are proposed. Then the discrete protocol is applied to the discrete-time system. Based on the Schur stability analysis of the system, the requirements of topology and parameter for the system to achieve enclosing control are given. Finally, the self-designed multi-agent platform is introduced, and simulation and experimental results are presented to validate the effectiveness of the protocol.