Adaptive Gradient Descent for Optimal Control of Parabolic Equations with Random Parameters

Yanzhao Cao; Somak Das; Hans-Werner van Wyk

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arXiv · 2110.10671

Adaptive Gradient Descent for Optimal Control of Parabolic Equations with Random Parameters

Yanzhao Cao·Somak Das·Hans-Werner van Wyk

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Abstract

In this paper we extend the adaptive gradient descent (AdaGrad) algorithm to the optimal distributed control of parabolic partial differential equations with uncertain parameters. This stochastic optimization method achieves an improved convergence rate through adaptive scaling of the gradient step size. We prove the convergence of the algorithm for this infinite dimensional problem under suitable regularity, convexity, and finite variance conditions, and relate these to verifiable properties of the underlying system parameters. Finally, we apply our algorithm to the optimal thermal regulation of lithium battery systems under uncertain loads.

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BibTeX RIS

Yanzhao Cao, Somak Das, Hans-Werner van Wyk. 2021-10-20. Adaptive Gradient Descent for Optimal Control of Parabolic Equations with Random Parameters. https://arxiv.org/abs/2110.10671

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