Abstract:Feedback optimization enables autonomous optimality seeking of a dynamical system through its closed-loop interconnection with iterative optimization algorithms. Among various iteration structures, model-based approaches require the input-output sensitivity matrix of the system to construct gradients, whereas model-free approaches eliminate this need by estimating gradients from real-time objective evaluations. These approaches offer complementary benefits in sample efficiency and accuracy against model mismatch, i.e., sensitivity errors. To achieve balanced closed-loop performance, we propose a gray-box feedback optimization controller, featuring systematic incorporation of approximate sensitivities into model-free updates via a tunable convex combination. We provide unified performance characterizations covering different approaches. We elucidate how cumulative sensitivity errors (model-based) and variances due to stochastic exploration (model-free) shape the closed-loop behavior and induce a trade-off between iteration and dimensional dependence. The proposed controller retains sample efficiency and provable (local) optimality for nonconvex problems despite inaccurate sensitivities. We further develop and characterize a running gray-box controller that handles constrained time-varying problems with changing objectives and steady-state input-output maps.
| Comments: | published in IEEE Transactions on Automatic Control, 2026 |
| Subjects: | Optimization and Control (math.OC); Systems and Control (eess.SY) |
| Cite as: | arXiv:2404.04355 [math.OC] |
| (or arXiv:2404.04355v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2404.04355 arXiv-issued DOI via DataCite |
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| Related DOI: | https://doi.org/10.1109/TAC.2026.3693174
DOI(s) linking to related resources |
From: Zhiyu He [view email]
[v1]
Fri, 5 Apr 2024 18:50:07 UTC (2,780 KB)
[v2]
Sun, 24 May 2026 12:41:58 UTC (518 KB)
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