Model-Free Methods for Optimal Group Containment Control of Multi-Agent Systems With Unknown Dynamics

For group containment control (GCC) problem, the presence of multiple subgroups and multiple leaders in each subgroup poses challenges for topology selection and problem analysis. This paper presents the endeavor to investigate the GCC problem of multi-agent systems with unknown dynamics, focusing specifically on optimizing its performance. First, the group neighborhood containment error is defined, and it is proven that the GCC can be achieved by converging the error to zero under the well-defined communication topology. Meanwhile, a feasible communication topology selection algorithm is proposed for GCC problem. Then, considering the optimization of control performance, the optimal GCC problem is formulated via optimality principle and graphical game by defining the local performance index for each agent. Based on adaptive dynamic programming, two novel online model-free methods are developed for solving optimal GCC problem, together with rigorous mathematical analysis. It is demonstrated that under the two methods, the optimal control policy can be learned using only system operation data, without requiring knowledge of system dynamics, thereby achieving the optimal GCC. Finally, corresponding simulation examples are executed to demonstrate the capacity of the developed methods.