Optimal discrete-time control for non-linear cascade systems

In this paper we develop an optimality-based framework for designing controllers for discrete-time non-linear cascade systems. Specifically, using a non-linear—non-quadratic optimal control framework we develop a family of globally stabilizing backstepping-type controllers parameterized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Bellman equation for the controlled system and thus guarantees both optimality and stability.