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Title: Online Optimization as a Feedback Controller: Stability and Tracking

Abstract

This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the algorithm is based on continuous-time primal-dual dynamics, properly modified to incorporate feedback from the LTI dynamical system, applied to a proximal augmented Lagrangian function. The resultant closed-loop algorithm tracks the solution of the time-varying optimization problem without requiring knowledge of (time-varying) disturbances in the dynamical system. The analysis leverages integral quadratic constraints to provide linear matrix inequality (LMI) conditions that guarantee global exponential stability and bounded tracking error. Analytical results show that, under a sufficient time-scale separation between the dynamics of the LTI dynamical system and the algorithm, the LMI conditions can be always satisfied. The paper further proposes a modified algorithm that can track an approximate solution trajectory of the constrained optimization problem under less restrictive assumptions. As an illustrative example, the proposed algorithms are showcased for power transmission systems, to compress the time scales between secondary and tertiary control, and allow to simultaneously power re-balancing and tracking of DC optimal power flow points.

Authors:
 [1];  [2];  [1]
  1. National Renewable Energy Lab. (NREL), Golden, CO (United States)
  2. Univ. of Colorado, Boulder, CO (United States)
Publication Date:
Research Org.:
National Renewable Energy Lab. (NREL), Golden, CO (United States)
Sponsoring Org.:
USDOE Office of Electricity, Advanced Grid Modeling Program
OSTI Identifier:
1526200
Report Number(s):
NREL/JA-5D00-72225
Journal ID: ISSN 2325-5870
Grant/Contract Number:  
AC36-08GO28308
Resource Type:
Accepted Manuscript
Journal Name:
IEEE Transactions on Control of Network Systems
Additional Journal Information:
Journal Name: IEEE Transactions on Control of Network Systems; Journal ID: ISSN 2325-5870
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; optimization; heuristic algorithms; time-varying systems; linear systems; control systems; steady-state; power system stability

Citation Formats

Colombino, Marcello, Dall'Anese, Emiliano, and Bernstein, Andrey. Online Optimization as a Feedback Controller: Stability and Tracking. United States: N. p., 2019. Web. doi:10.1109/TCNS.2019.2906916.
Colombino, Marcello, Dall'Anese, Emiliano, & Bernstein, Andrey. Online Optimization as a Feedback Controller: Stability and Tracking. United States. doi:10.1109/TCNS.2019.2906916.
Colombino, Marcello, Dall'Anese, Emiliano, and Bernstein, Andrey. Mon . "Online Optimization as a Feedback Controller: Stability and Tracking". United States. doi:10.1109/TCNS.2019.2906916.
@article{osti_1526200,
title = {Online Optimization as a Feedback Controller: Stability and Tracking},
author = {Colombino, Marcello and Dall'Anese, Emiliano and Bernstein, Andrey},
abstractNote = {This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the algorithm is based on continuous-time primal-dual dynamics, properly modified to incorporate feedback from the LTI dynamical system, applied to a proximal augmented Lagrangian function. The resultant closed-loop algorithm tracks the solution of the time-varying optimization problem without requiring knowledge of (time-varying) disturbances in the dynamical system. The analysis leverages integral quadratic constraints to provide linear matrix inequality (LMI) conditions that guarantee global exponential stability and bounded tracking error. Analytical results show that, under a sufficient time-scale separation between the dynamics of the LTI dynamical system and the algorithm, the LMI conditions can be always satisfied. The paper further proposes a modified algorithm that can track an approximate solution trajectory of the constrained optimization problem under less restrictive assumptions. As an illustrative example, the proposed algorithms are showcased for power transmission systems, to compress the time scales between secondary and tertiary control, and allow to simultaneously power re-balancing and tracking of DC optimal power flow points.},
doi = {10.1109/TCNS.2019.2906916},
journal = {IEEE Transactions on Control of Network Systems},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {3}
}

Journal Article:
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This content will become publicly available on March 25, 2020
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