Linear ordinary differential equations constrained Gaussian Processes for solving optimal control problems

Abstract

This paper presents an intrinsic approach for addressing control problems with systems governed by linear ordinary differential equations (ODEs). We use computer algebra to constrain a Gaussian Process on solutions of ODEs. We obtain control functions via conditioning on datapoints. Our approach thereby connects Algebra, Functional Analysis, Machine Learning and Control theory. We discuss the optimality of the control functions generated by the posterior mean of the Gaussian Process. We present numerical examples which underline the practicability of our approach.