Game-based enclosing control of multi-agent systems

The enclosing control of multi-agent systems is considered in this paper based on game modeling. First, the agents’ interactions within the multi-agent system are formulated as a multi-player game. The cost functions are designed for leaders and followers, respectively. At each time step, the state evolution of the agents is driven by the Nash equilibrium of the proposed game. Second, the unique Nash equilibrium is proved and calculated for the proposed multi-player game. Moreover, the relationship between the states of two neighboring game times is established for the multi-agent system. Then, using graph theory and matrix theory, conditions for the multi-agent system achieving enclosing control are provided. Finally, several examples of simulations are shown to verify the mathematical results.