A multiobjective optimization approach for optimal control problems of mechanical systems with uncertainties

This work deals with the optimal control of mechanical systems with uncertainties which are associated to e.g. unknown parameters such as friction coefficients or geometry parameters in the model. While in the deterministic setting we characterize the maximal performance of the control system by fulfilling a predefined task exactly, in presence of uncertainty a performance measure is introduced whose mean has to be minimized to guarantee maximal performance of the control system. Taking this notion of system performance as additional objective into account leads to a multiobjective optimal control problem. Based on techniques from multiobjective optimization we present a methodology to numerically approximate the set of Pareto optimal solutions. The approach is verified by means of a robot arm maneuver with uncertain model parameters.