Graph-based strategies for multi-player pursuit evasion games

Maximization of the second smallest eigenvalue of the graph Laplacian has recently been studied in the field of cooperative control. Instead of the second smallest eigenvalue, we design a gradient-based control law for multiple agents to maximize an arbitrary nonzero eigenvalue. The gradient of an eigenvalue is derived through a standard sensitivity analysis. Furthermore, connections are drawn between the connectivity control and pursuit-evasion (PE) problems with multiple players. A gradient-based strategy is designed and the performance is verified by simulations. A comparison with the previously designed suboptimal strategy is provided. This is a preliminary study of a graph theoretical approach to multi-player PE problems.