Robust Optimal Control of Nonlinear Systems via Homotopy Shooting Method

This paper introduces an algorithm for solving robust optimal controllers for nonlinear systems using the homotopy shooting method. Robustness is ensured by penalizing the sensitivity states of the models during the transition and at the final time. In two examples, the cost is represented by the tracking error and terminal residual energy for a rest-to-rest maneuver. The proposed approach is illustrated on a double mass-spring-damper system and on a Type 1 Diabetes model where the cost function includes the integral of the tracking error. Our method can be readily extended for de-sensitization of multiple states over the whole time interval.