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Adaptive Online Model Update Algorithm for Predictive Control in Networked Systems

Vivek Khatana, Chin-Yao Chang, Wenbo Wang

TL;DR

The paper tackles the challenge of online, distributed model updates for predictive control in networked systems, with a focus on power distribution. It introduces an online gradient-descent algorithm that updates a parameterized input-output map in real time, enabling better closed-loop performance while reducing communication bandwidth and preserving local privacy. A distributed reformulation is provided, with a sublinear regret guarantee $\mathcal{R}_T = O(\sqrt{T})$, and a fusion-center-assisted implementation is described. The approach is validated on a voltage-regulation problem using a modified IEEE 37-bus system, showing that a nonlinear convex model can outperform linear approximations in maintaining voltage within limits in the presence of disturbances and variable generation.

Abstract

In this article, we introduce an adaptive online model update algorithm designed for predictive control applications in networked systems, particularly focusing on power distribution systems. Unlike traditional methods that depend on historical data for offline model identification, our approach utilizes real-time data for continuous model updates. This method integrates seamlessly with existing online control and optimization algorithms and provides timely updates in response to real-time changes. This methodology offers significant advantages, including a reduction in the communication network bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt after disturbances. Furthermore, our algorithm is tailored for non-linear convex models, enhancing its applicability to practical scenarios. The efficacy of the proposed method is validated through a numerical study, demonstrating improved control performance using a synthetic IEEE test case.

Adaptive Online Model Update Algorithm for Predictive Control in Networked Systems

TL;DR

The paper tackles the challenge of online, distributed model updates for predictive control in networked systems, with a focus on power distribution. It introduces an online gradient-descent algorithm that updates a parameterized input-output map in real time, enabling better closed-loop performance while reducing communication bandwidth and preserving local privacy. A distributed reformulation is provided, with a sublinear regret guarantee , and a fusion-center-assisted implementation is described. The approach is validated on a voltage-regulation problem using a modified IEEE 37-bus system, showing that a nonlinear convex model can outperform linear approximations in maintaining voltage within limits in the presence of disturbances and variable generation.

Abstract

In this article, we introduce an adaptive online model update algorithm designed for predictive control applications in networked systems, particularly focusing on power distribution systems. Unlike traditional methods that depend on historical data for offline model identification, our approach utilizes real-time data for continuous model updates. This method integrates seamlessly with existing online control and optimization algorithms and provides timely updates in response to real-time changes. This methodology offers significant advantages, including a reduction in the communication network bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt after disturbances. Furthermore, our algorithm is tailored for non-linear convex models, enhancing its applicability to practical scenarios. The efficacy of the proposed method is validated through a numerical study, demonstrating improved control performance using a synthetic IEEE test case.
Paper Structure (11 sections, 3 theorems, 36 equations, 4 figures, 3 algorithms)

This paper contains 11 sections, 3 theorems, 36 equations, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Definition and Notations
  4. Agent Based System Framework
  5. Model Update Problem and the Distributed Reformulation
  6. Online Model Update Algorithm
  7. Controller with Online Model Updates
  8. Application Example and Numerical Simulations
  9. Power System Application Example
  10. Illustrative Numerical Simulations
  11. Conclusion

Key Result

Lemma 1

(Optimal solutions of eq:intermediate_opt_problem and eq:modified_prob). Let the matrix $\widehat{\mathbf{P}}$ in eq:modified_prob be such that $\mathbf{P}$ satisfy Assumption assmp:null_space. If $\mathbf{x}^\star = [\theta^\star ; w^\star]$ is a solution to problem eq:modified_prob, then $\theta^\

Figures (4)

  • Figure 1: Schematic of the modified IEEE 37 bus system. The buses highlighted in red triangles are PES buses
  • Figure 2: The voltage magnitudes ($p.u.$) over time in the modified IEEE $37$-bus system without any control.
  • Figure 3: The voltage magnitudes ($p.u.$) over time in the modified IEEE $37$-bus system with control decisions derived using the online distributed estimated linear map between power injections and voltage magnitudes.
  • Figure 4: The voltage magnitudes ($p.u.$) over time in the modified IEEE $37$-bus system with control decisions derived using a non-linear map between power injections and voltage magnitudes updated online.

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof