On competitive control systems

Unlike conventional control systems, the competitive control systems (CCS) have several groups of controls and each group of controls have their own control purpose. The “optimal solutions” for CCS can only be Nash equilibriums. In this paper three kinds of CCS´s are considered. First of all, we consider the game-based discrete-time CCS. The topology of mix-valued logical networks is investigated, and certain conditions for the optimal solution are obtained. Secondly, the continuous-time CCS´s are considered. Coupled Hamilton-Jacobi-Bellman equations are proposed for the best reaction functions. Finally, the multi-purpose control problems are considered. The “best” solution is explored by converting them to CCS.