Graph-based strategies for multi-player pursuit evasion games
Dongxu Li, Jose B. Cruz · 2007
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 multiplayer PE problems.