Multi-cumulant and pareto strategies for stochastic multi-player pursuit-evasion

The paper presents an extension of cumulant-based control theory over a finite horizon for a class of multi-player pursuit-evasion wherein the evolution of the states of the game in response to adversarial strategies selected by pursuit and evasion teams from the efficient Pareto sets of admissible strategies is described by a stochastic linear differential equation and an integral-quadratic performance-measure. Both cooperation within each team and competition between the teams presumably exist. A direct dynamic programming approach for the Mayer optimization problem is used to solve for a multi-cumulant and Pareto-based solution when the members in each team optimally implement collective strategies and effectively shape the distribution of their Chi-squared random measures of performance associated with this special class of stochastic multi-player pursuit-evasion games.