Model-Free $\mu$-Synthesis: A Nonsmooth Optimization Perspective

• URL: http://arxiv.org/abs/2402.11654v1
• Date: Sun, 18 Feb 2024 17:17:17 GMT
• Title: Model-Free $\mu$-Synthesis: A Nonsmooth Optimization Perspective
• Authors: Darioush Keivan, Xingang Guo, Peter Seiler, Geir Dullerud, Bin Hu
• Abstract summary: In this paper, we revisit an important policy search benchmark, namely $mu$-synthesis. We show that subgradient-based search methods have led to impressive numerical results in practice.
• Score: 4.477225073240389
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we revisit model-free policy search on an important robust control benchmark, namely $\mu$-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 $\mu$-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 $\mu$-synthesis problems in the model-free setting.

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