Open-loop Nash equilibrium for networked control systems with asymmetric information

This paper focuses on the open-loop Nash equilibrium for networked control systems (NCSs) with asymmetric information. In this NCSs model, player 1 shares its observations and historical control inputs with player 2, whereas player 2 does not disclose any of its information to player 1. Using the maximum principle, we obtain an explicit analytical Nash equilibrium by decoupling solving the forward and backward stochastic difference equations (FBSDEs), while the optimal gain matrices are given by coupled Riccati equations. The asymmetric information leads to coupled forward and backward Riccati equations, which complicates the calculation. To address it, a forward iteration algorithm is employed to obtain a suboptimal solution for the open-loop Nash equilibrium strategy with asymmetric information. Numerical results illustrate that incorporating the Nash equilibrium into NCSs can improve the system performance.