Online Optimization as a Feedback Controller: Stability and Tracking

Journal Article · Mon Mar 25 00:00:00 EDT 2019 · IEEE Transactions on Control of Network Systems

DOI:https://doi.org/10.1109/TCNS.2019.2906916· OSTI ID:1526200

Colombino, Marcello ^[1]; Dall'Anese, Emiliano ^[2]; Bernstein, Andrey ^[1]

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1. National Renewable Energy Lab. (NREL), Golden, CO (United States)
2. Univ. of Colorado, Boulder, CO (United States)

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.

• Research Organization: National Renewable Energy Laboratory (NREL), Golden, CO (United States)
• Sponsoring Organization: USDOE Office of Electricity, Advanced Grid Modeling Program
• Grant/Contract Number: AC36-08GO28308
• OSTI ID: 1526200
• Report Number(s): NREL/JA-5D00-72225; MainId:20799; UUID:b1ee3f26-dea0-e811-9c16-ac162d87dfe5; MainAdminID:9275
• Journal Information: IEEE Transactions on Control of Network Systems, Journal Name: IEEE Transactions on Control of Network Systems Journal Issue: 1 Vol. 7; ISSN 2325-5870
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

24 POWER TRANSMISSION AND DISTRIBUTION
control systems
heuristic algorithms
linear systems
optimization
power system stability
steady-state
time-varying systems