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

TL;DR

This paper introduces a model-free, feedback-based optimization method called P-PDZD that uses output feedback to solve constrained problems without knowing the system model, applicable to multi-agent systems and verified in power systems.

Contribution

The paper develops a novel model-free primal-dual dynamics approach with stability guarantees and decentralized implementation for multi-agent systems.

Findings

Achieves semi-global practical asymptotic stability.

Handles both hard and asymptotic constraints effectively.

Demonstrates robustness and adaptivity in power system voltage control.

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.