Resilient cumulant game control for cyber-physical systems

In this paper, we investigate the resilient cumulant game control problem for a cyber-physical system. The cyberphysical system is modeled as a linear hybrid stochastic system with full-state feedback. We are interested in 2-player cumulant Nash game for a linear Markovian system with quadratic cost function where the players optimize their system performance by shaping the distribution of their cost function through cost cumulants. The controllers are optimally resilient against control feedback gain variations.We formulate and solve the coupled first and second cumulant Hamilton-Jacobi-Bellman (HJB) equations for the dynamic game. In addition, we derive the optimal players strategy for the second cost cumulant function. The efficiency of our proposed method is demonstrated by solving a numerical example.