In this paper we develop an optimality-based framework for designing controllers for discrete-time nonlinear cascade systems. Specifically, using a nonlinear-nonquadratic 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.
Journal of the Franklin Institute
Abdallah, Chaouki T.; W. M. Haddad; J. L. Fausz; and V. Chellaboina. "Optimal discrete-time control for non-linear cascade systems." Journal of the Franklin Institute 335, 5 (1998): 827-839. http://digitalrepository.unm.edu/ece_fsp/67