In this paper we develop an optimality-based framework for backstepping controllers. Specifically, using a nonlinear-nonquadratic optimal control framework we develop a family of globally stabilizing backstepping controllers parametrized 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 Hamilton-Jacobi-Bellman equation for the controlled system and thus guarantees both optimality and stability. The results are specialized to the case of integrator backstepping.
Proceedings of the 36th IEEE Conference on Decision and Control
Backstepping, Control nonlinearities, Linear feedback control systems
Abdallah, Chaouki T.; Wassim M. Haddad; Jerry L. Fausz; and Vijaya-Sekhar Chellaboina. "A unification between nonlinear-nonquadratic optimal control and integrator backstepping." Proceedings of the 36th IEEE Conference on Decision and Control (1997): 1741-1742. doi:10.1109/CDC.1997.657808.