In this work, we consider some issues concerning the minimax optimal control problem with continuous time and infinite horizon. The minimax optimal control problem has been analyzed in recent publications from different points of view. For the theoretical analysis of the finite horizon problem (fhp), we can see [6] arid [7, 10]; the numerical analysis of the fhp has been done in [12, 13]. Extensions has been considered in [1, 2, 3, 8, 9, 17]. The open loop necessary conditions of optimality has been presented in [4]. In the infinite horizon problem (ihp), the analysis of the optimal cost function and its approximate computation present considerable difficulties. Particularly, characterizing it through the Hamilton-Jacobi-Bellman (HJB) equation requires a careful treatment because the optimal cost function has poor properties of regularity and, even in its integral form, the HJB equation has riot unique solution. In [11, 14, 15] we have considered the ihp and we have analyzed some properties of the optimal cost function among them, the issue of regularity and the approximation with finite horizon problems. We have also proved in [14] that the optimal cost function is characterized as the lowest supersolution and as the maximum element of a special class of subsolutions of the associated HJB equation. In this work, other issues concerning the infinite horizon case are analyzed.
展开▼
