A unification between nonlinear-nonquadratic optimal control and integrator backstepping

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