Two-player ad hoc output-feedback cumulant game control

This paper studies a finite horizon output-feedback game control problem where two players seek to optimize their system performance by shaping the distribution of their cost function through cost cumulants. We consider a two-player second cumulant nonzero-sum Nash game for a partially-observed linear system with quadratic cost function. We derive the near-optimal players strategy for the second cost cumulant function by solving the Hamilton-Jacobi-Bellman (HJB) equation. The results of the proposed approach are demonstrated by solving a numerical example.