A framework for randomized time-splitting in linear-quadratic optimal control

Veldman D, Zuazua Iriondo E (2022)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2022

Journal

Numerische Mathematik Springer Verlag (Germany)

Publisher: Springer

Book Volume: 151

Pages Range: 495–549

Journal Issue: 2

URI: https://link.springer.com/article/10.1007/s00211-022-01290-3

DOI: 10.1007/s00211-022-01290-3

Open Access Link: https://link.springer.com/article/10.1007/s00211-022-01290-3

Abstract

Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal control. In our proposed framework, the linear dynamics of the original problem is replaced by a randomized dynamics. To obtain the randomized dynamics, the system matrix is split into simpler submatrices and the time interval of interest is split into subintervals. The randomized dynamics is then found by selecting randomly one or more submatrices in each subinterval.

We show that the dynamics, the minimal values of the cost functional, and the optimal control obtained with the proposed randomized time-splitting method converge in expectation to their analogues in the original problem when the time grid is refined. The derived convergence rates are validated in several numerical experiments. Our numerical results also indicate that the proposed method can lead to a reduction in computational cost for the simulation and optimal control of large-scale linear dynamical systems.

Authors with CRIS profile

Daniël Willem Maria Veldman Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Veldman, D., & Zuazua Iriondo, E. (2022). A framework for randomized time-splitting in linear-quadratic optimal control. Numerische Mathematik, 151(2), 495–549. https://dx.doi.org/10.1007/s00211-022-01290-3

MLA:

Veldman, Daniel, and Enrique Zuazua Iriondo. "A framework for randomized time-splitting in linear-quadratic optimal control." Numerische Mathematik 151.2 (2022): 495–549.

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