Model-Free $μ$-Synthesis: A Nonsmooth Optimization Perspective Article Swipe

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Darioush Keivan , Xingang Guo , Peter Seiler , Geir E. Dullerud , Bin Hu ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2402.11654

In this paper, we revisit model-free policy search on an important robust control benchmark, namely $μ$-synthesis. In the general output-feedback setting, there do not exist convex formulations for this problem, and hence global optimality guarantees are not expected. Apkarian (2011) presented a nonconvex nonsmooth policy optimization approach for this problem, and achieved state-of-the-art design results via using subgradient-based policy search algorithms which generate update directions in a model-based manner. Despite the lack of convexity and global optimality guarantees, these subgradient-based policy search methods have led to impressive numerical results in practice. Built upon such a policy optimization persepctive, our paper extends these subgradient-based search methods to a model-free setting. Specifically, we examine the effectiveness of two model-free policy optimization strategies: the model-free non-derivative sampling method and the zeroth-order policy search with uniform smoothing. We performed an extensive numerical study to demonstrate that both methods consistently replicate the design outcomes achieved by their model-based counterparts. Additionally, we provide some theoretical justifications showing that convergence guarantees to stationary points can be established for our model-free $μ$-synthesis under some assumptions related to the coerciveness of the cost function. Overall, our results demonstrate that derivative-free policy optimization offers a competitive and viable approach for solving general output-feedback $μ$-synthesis problems in the model-free setting.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2402.11654
PDF: https://arxiv.org/pdf/2402.11654
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4391984881

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DOI: https://doi.org/10.48550/arxiv.2402.11654

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Title: Model-Free $μ$-Synthesis: A Nonsmooth Optimization Perspective

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-02-18

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Authors: Darioush Keivan, Xingang Guo, Peter Seiler, Geir E. Dullerud, Bin Hu

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Landing page: https://arxiv.org/abs/2402.11654

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Concepts: Perspective (graphical), Computer science, Mathematical economics, Mathematical optimization, Mathematics, Artificial intelligence

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