Robust nonlinear optimal control of dynamic systems with affine uncertainties

In this paper we present novel strategies to formulate and solve nonlinear robust optimal control problems for dynamic systems which are affine in the uncertainty. We suggest the definition of a constrained Lyapunov differential equation providing robustness interpretations with respect to L₂-bounded disturbances in the context of inequality state constraints. This interpretation allows us to compute the robust counterpart formulation for optimal control problems which are affine in the uncertainty. Furthermore, we demonstrate the applicability of the presented formulation for a numerical test example: a crane should carry a mass from one to another point while an unknown force excites the open-loop controlled system. The robustly optimized input allows us to control the mass to a target region while satisfying inequality constraints on the worst-case excitation.