A Gaussian Process Learning Method for Nonlinear Optimal Control

This thesis is focused on discrete-time nonlinear optimal control techniques enhanced via a supervised learning approach based on Gaussian Process regression. Since optimal control strategies are strongly model-based, a perfect knowledge of the real system is required in order to obtain the best performances; however, it is not always possible to satisfy these requirements, since model uncertainties due to, e.g., unavailable information or hard to model dynamical effects may be present leading to a suboptimal solution for the real problem. The basic idea is to exploit measurement data to reduce (and possibly mitigate) model uncertainty. In this context, a machine learning tool, Gaussian Processes, provides a flexible and easy tool to directly assess the residual model uncertainty and to enhance the control performances. In this work, Sequential Open Loop and Differential Dynamic Programming, two well-known optimal control strategies, are adapted such that to include Gaussian Process regression. The resulting strategies adopt a simultaneous approach: at each iteration, an optimization step is executed such that a trajectory with a lower cost than the previous one is obtained. Then a learning step is performed, in order to collect data which improve the regression for next iterations. Thanks to Gaussian Process regression, the new strategies are able to solve optimal control problems when model uncertainties are present. Furthermore, the learning part is enhanced by including a selection policy which rejects not useful measurements, such that to speed-up the resolution and to assure more stability to the algorithm.