Regulation of Dynamical Systems to Optimal Solutions of Semidefinite Programs: Algorithms and Applications to AC Optimal Power Flow

TL;DR

This paper develops a dual epsilon-subgradient based feedback control method for networked nonlinear systems, ensuring convergence to optimal solutions of SDPs, with applications to AC power flow control.

Contribution

It introduces a novel control framework that guarantees convergence to SDP solutions in networked systems, bridging real-time control and optimization.

Findings

Guarantees global convergence with diminishing stepsize rules.

Applies to control of power-electronic inverters in AC systems.

Bridges time-scale separation between control and optimization.

Abstract

This paper considers a collection of networked nonlinear dynamical systems, and addresses the synthesis of feedback controllers that seek optimal operating points corresponding to the solution of network-wide constrained optimization problems. Particular emphasis is placed on the solution of semidefinite programs (SDPs). The design of the feedback controller is grounded on a dual epsilon-subgradient approach, with the dual iterates utilized to dynamically update the dynamical-system reference signals. Global convergence is guaranteed for diminishing stepsize rules, even when the reference inputs are updated at a faster rate than the dynamical-system settling time. The application of the proposed framework to the control of power-electronic inverters in AC distribution systems is discussed. The objective is to bridge the time-scale separation between real-time inverter control and network-wide optimization. Optimization objectives assume the form of SDP relaxations of prototypical AC optimal power flow problems.