Game-based inner approximation of maximal output admissible sets under references unknown in advance

This paper proposes a game-based inner approximation method that efficiently arranges multiple ellipsoids approximating a parameterization of maximal output admissible sets in terms of a reference vector. The approximation is contributive when considering a tracking control problem for constrained systems in which a reference value is not given in advance. Our idea for the approximation is to characterize search points of the ellipsoids in a state based game and a log-linear learning algorithm by dynamics of the constrained system. Consequently, an efficient arrangement of the ellipsoids can be achieved at a lower computation cost. A numerical example is finally illustrated to make sure of the consequence, compared to our previous works.