Semiglobal nonlinear stabilization via approximate policy iteration

We consider the problem of semiglobal nonlinear stabilization. Based on a given up table dynamic system and a region of acceptable operation within which the state is desired to be confined, we define an appropriate alternative dynamic system. We define an optimal control problem for the alternative (redefined) system which is amenable to solution via approximate policy iteration (a computational design procedure for suboptimal control design). We show that the optimal controller for the alternative problem is stabilizing for the original system, provided that the latter is stabilizable. It follows that the suboptimal controllers designed via approximate policy iteration are stabilizing for the original system, for sufficiently small approximation errors