Probabilistic Invariance for Gaussian Process State Space Models

Gaussian process state space models are becoming common tools for the analysis and design of nonlinear systems with uncertain dynamics. When designing control policies for these systems, safety is an important property to consider. In this paper, we provide safety guarantees for Gaussian process state space models in the form of probabilistic invariant sets, where the state trajectory is guaranteed to lie within an invariant set for all time with a particular probability. We provide a sufficient condition in the form of a linear matrix inequality to evaluate the probabilistic invariance of the system, and we demonstrate our contributions with an illustrative example.