Model-Free $μ$-Synthesis: A Nonsmooth Optimization Perspective
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914684793257984 |
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| author | Keivan, Darioush Guo, Xingang Seiler, Peter Dullerud, Geir Hu, Bin |
| author_facet | Keivan, Darioush Guo, Xingang Seiler, Peter Dullerud, Geir Hu, Bin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11654 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model-Free $μ$-Synthesis: A Nonsmooth Optimization Perspective Keivan, Darioush Guo, Xingang Seiler, Peter Dullerud, Geir Hu, Bin Optimization and Control Machine Learning 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. |
| title | Model-Free $μ$-Synthesis: A Nonsmooth Optimization Perspective |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2402.11654 |