On Computation of Numerical Solutions to Hamilton-Jacobi Inequalities Using Gaussian Process Regression

摘要

This paper proposes numerical solutions of Hamilton-Jacobi inequalities based on constrained Gaussian process regression. In the proposed method, probability functions of the solutions to the Hamilton-Jacobi inequalities are derived by Gaussian process regression with additional equality and inequality constraints to cope with partial differential inequalities. In addition, hyper parameters are optimized using an empirical gradient method.