Optimal nonlinear disturbance rejection control for nonlinear cascade systems

We develop an optimality-based disturbance rejection control framework for nonlinear cascade systems with bounded energy (square-integrable) L₂ disturbances. Specifically, using a nonlinear-nonquadratic disturbance rejection optimal control framework we develop a family of globally stabilizing generalized 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. In addition, the resulting optimal controller guarantees that the closed-loop system is non-expansive (gain bounded). The results are then used to design disturbance rejection controllers for jet engine compression systems with bounded energy L₂ disturbances