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arXiv · 2301.00419

Policy iteration for the deterministic control problems -- a viscosity approach

Wenpin Tang·Hung Vinh Tran·Yuming Paul Zhang
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Abstract

This paper is concerned with the convergence rate of policy iteration for (deterministic) optimal control problems in continuous time. To overcome the problem of ill-posedness due to lack of regularity, we consider a semi-discrete scheme by adding a viscosity term via finite differences in space. We prove that PI for the semi-discrete scheme converges exponentially fast, and provide a bound on the error induced by the semi-discrete scheme. We also consider the discrete space-time scheme, where both space and time are discretized. Convergence rate of PI and the discretization error are studied.

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Wenpin Tang, Hung Vinh Tran, Yuming Paul Zhang. 2023-01-01. Policy iteration for the deterministic control problems -- a viscosity approach. https://arxiv.org/abs/2301.00419

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