Hybrid Optimal Control for Dynamical Systems using Gaussian Process Regression and Unscented Transform*

In this paper we present a new approach to determine optimal control sequences for nonlinear systems with imperfect or partial knowledge about their dynamics. In this scenario, classical procedures recommend a more complex analytical modeling design, an effort that may be time consuming due to the acquisition of expertise or possibly not applicable. Our hybrid
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optimal control design compensates for model errors using Gaussian processes learned from measured system data, thus overcoming the limitations of the classical methodology. The associated hybrid optimal control problem is set up and solved using the unscented transform and the multiple shooting approach, making our developed method flexible, data-efficient, and robust. Relevant practical implementation details are explained and an optimal control is exemplary designed for a fully actuated double pendulum, where we analyze the results and draw a comparison between an application with and without existing prior knowledge.