On the Numerical Solution of a Class of Pursuit-Evasion Games

This paper presents a new computational approach for a class of pursuit-evasion games of degree. The saddle-point problem is decomposed into two subproblems that are solved by turns iteratively. The subproblems are ordinary optimal control problems that can be solved efficiently using discretization and nonlinear programming techniques. Hence it is not necessary to supply an initial guess of the adjoint variables or a hypothesis on the switching structure of the solution. Furthermore, in the presented approach the numerical differentiation of the payoff is avoided. We test the algorithm with different numerical examples and compare the results with solutions obtained by an indirect method. In the test examples the method converges rapidly from a rough initial guess, and the results coincide well with the reference solutions.