Publikation: Optimal Feedback Law Recovery by Gradient-Augmented Sparse Polynomial Regression
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2021
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Journal of Machine Learning Research (JMLR). Microtome Publishing. 2021, 22, 48. ISSN 1532-4435. eISSN 1533-7928
Zusammenfassung
A sparse regression approach for the computation of high-dimensional optimal feedback laws arising in deterministic nonlinear control is proposed. The approach exploits the control-theoretical link between Hamilton-Jacobi-Bellman PDEs characterizing the value function of the optimal control problems, and rst-order optimality conditions via Pontryagin's Maximum Principle. The latter is used as a representation formula to recover the value function and its gradient at arbitrary points in the space-time domain through the solution of a two-point boundary value problem. After generating a dataset consisting of di erent state-value pairs, a hyperbolic cross polynomial model for the value function is tted using a LASSO regression. An extended set of low and high-dimensional numerical tests in nonlinear optimal control reveal that enriching the dataset with gradient information reduces the number of training samples, and that the sparse polynomial regression consistently yields a feedback law of lower complexity.
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004 Informatik
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Optimal Feedback Control, Optimality Conditions, Hamilton-Jacobi-Bellman PDE, Polynomial Approximation, Sparse Optimization
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AZMI, Behzad, Dante KALISE, Karl KUNISCH, 2021. Optimal Feedback Law Recovery by Gradient-Augmented Sparse Polynomial Regression. In: Journal of Machine Learning Research (JMLR). Microtome Publishing. 2021, 22, 48. ISSN 1532-4435. eISSN 1533-7928BibTex
@article{Azmi2021Optim-56521,
year={2021},
title={Optimal Feedback Law Recovery by Gradient-Augmented Sparse Polynomial Regression},
url={https://jmlr.org/papers/v22/20-755.html},
volume={22},
issn={1532-4435},
journal={Journal of Machine Learning Research (JMLR)},
author={Azmi, Behzad and Kalise, Dante and Kunisch, Karl},
note={Article Number: 48}
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2022-02-10
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