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arXiv · 2206.11123

Model-Free Feedback Constrained Optimization Via Projected Primal-Dual Zeroth-Order Dynamics

Xin Chen·Jorge I. Poveda·Na Li
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Abstract

In this paper, we propose a model-free feedback solution method to solve generic constrained optimization problems, without knowing the specific formulations of the objective and constraint functions. This solution method is termed projected primal-dual zeroth-order dynamics (P-PDZD) and is developed based on projected primal-dual gradient dynamics and extremum seeking control. In particular, the P-PDZD method can be interpreted as a model-free controller that autonomously drives an unknown system to the solution of the optimization problem using only output feedback. The P-PDZD can properly handle both the hard and asymptotic constraints, and we develop the decentralized version of P-PDZD when applied to multi-agent systems. Moreover, we prove that the P-PDZD achieves semi-global practical asymptotic stability and structural robustness. We then apply the decentralized P-PDZD to the optimal voltage control problem in power distribution systems with square probing signals, and the simulation results verified the optimality, robustness, and adaptivity of the P-PDZD method.

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Xin Chen, Jorge I. Poveda, Na Li. 2022-06-22. Model-Free Feedback Constrained Optimization Via Projected Primal-Dual Zeroth-Order Dynamics. https://arxiv.org/abs/2206.11123

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