Scenario-based Optimal Control for Gaussian Process State Space Models

Abstract

Data-driven approaches from machine learning provide powerful tools to identify dynamical systems with limited prior knowledge of the model structure. More particular, the Gaussian process state space model, a Bayesian nonparametric approach, is increasingly utilized in control. Its probabilistic nature is interpreted differently in the control literature, but so far, it is not considered as a distribution over dynamical system which allows a scenario-based control design. This paper introduces how scenarios are sampled from a Gaussian process and utilizes them in a differential dynamic programming approach to solve an optimal control problem. For the linear-quadratic case, we derive probabilistic performance guarantees using results from robust convex optimization. The proposed methods are evaluated numerically for the nonlinear and linear case.