A Study on Solutions to Finite-Time Optimal Control Problems by Numerical Gaussian Processes

This paper proposes solutions to finite-time optimal control problems based on numerical Gaussian processes. In the proposed method, Hamilton-Jacobi-Bellman (HJB) equations are formulated using Euler method to be solved by numerical Gaussian processes. In order to incorporate information of systems into Gaussian processes, the covariance functions are structured explicitly by HJB equations.