Adaptive stochastic gradient descent for optimal control of parabolic equations with random parameters. Issue 6 (3rd February 2022)

• Record Type: Journal Article
• Authors: Cao, Yanzhao; Das, Somak; van Wyk, Hans‐Werner
• Other Names: Bochev Pavel guestEditor.; D'Elia Marta guestEditor.; Du Qiang guestEditor.; Hou Steve guestEditor.; Webster Clayton guestEditor.; Zhang Guannan guestEditor.
• Is Part Of: Numerical methods for partial differential equations. Volume 38:Issue 6(2022)
• Page Start: 2104
• Page End: 2122
• Publication Date: 2022-02-03
• Subjects: optimal control -- stochastic optimization -- thermal regulation -- uncertain systems; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22869
• Languages: English
• ISSNs: 0749-159X

Abstract

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.