SICE Journal of Control, Measurement, and System Integration
Online ISSN : 1884-9970
Print ISSN : 1882-4889
ISSN-L : 1882-4889
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Numerical Solutions of Hamilton-Jacobi Inequalities by Constrained Gaussian Process Regression
Kenji FUJIMOTOHirofumi BEPPUYuji TAKAKI
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2018 Volume 11 Issue 5 Pages 419-428

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Abstract

This paper proposes numerical solutions of Hamilton-Jacobi inequalities based on constrained Gaussian process regression. While Gaussian process regression is a tool to estimate an unknown function from its input and output data conventionally, the proposed method applies it to solving a known partial differential inequality. This is done by generating sample data pairs of states and corresponding values of the unknown function satisfying the inequality. A formal algorithm to execute such a procedure to obtain the probability of a solution to the Hamilton-Jacobi inequality is proposed. In addition, a nonstationary covariance function is introduced to increase the accuracy of the solutions and to reduce the computational cost. Furthermore, its hyper parameters are optimized using an empirical gradient method.

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© 2018 The Society of Instrument and Control Engineers
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