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Distributed Optimization under Edge Agreement with Application in Battery Network Management

Zehui Lu, Shaoshuai Mou

TL;DR

A discrete-time algorithm is proposed to solve a distributed optimization problem under edge agreements, providing a theoretical analysis to prove its convergence and illustrating the connection between the theory of distributed optimization under edge agreements and distributed model predictive control through a distributed battery network energy management problem.

Abstract

This paper investigates a distributed optimization problem under edge agreements, where each agent in the network is also subject to local convex constraints. Generalized from the concept of consensus, a group of edge agreements represents the constraints defined for neighboring agents, with each pair of neighboring agents required to satisfy one edge agreement constraint. Edge agreements are defined locally to allow more flexibility than a global consensus, enabling heterogeneous coordination within the network. This paper proposes a discrete-time algorithm to solve such problems, providing a theoretical analysis to prove its convergence. Additionally, this paper illustrates the connection between the theory of distributed optimization under edge agreements and distributed model predictive control through a distributed battery network energy management problem. This approach enables a new perspective to formulate and solve network control and optimization problems.

Distributed Optimization under Edge Agreement with Application in Battery Network Management

TL;DR

A discrete-time algorithm is proposed to solve a distributed optimization problem under edge agreements, providing a theoretical analysis to prove its convergence and illustrating the connection between the theory of distributed optimization under edge agreements and distributed model predictive control through a distributed battery network energy management problem.

Abstract

This paper investigates a distributed optimization problem under edge agreements, where each agent in the network is also subject to local convex constraints. Generalized from the concept of consensus, a group of edge agreements represents the constraints defined for neighboring agents, with each pair of neighboring agents required to satisfy one edge agreement constraint. Edge agreements are defined locally to allow more flexibility than a global consensus, enabling heterogeneous coordination within the network. This paper proposes a discrete-time algorithm to solve such problems, providing a theoretical analysis to prove its convergence. Additionally, this paper illustrates the connection between the theory of distributed optimization under edge agreements and distributed model predictive control through a distributed battery network energy management problem. This approach enables a new perspective to formulate and solve network control and optimization problems.
Paper Structure (12 sections, 6 theorems, 74 equations, 5 figures, 1 table, 2 algorithms)

This paper contains 12 sections, 6 theorems, 74 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Assumptions
  4. Algorithm and Analysis
  5. Proposed Distributed Algorithm
  6. Theoretical Analysis
  7. Numerical Simulation
  8. Application: Distributed Battery Network Energy Management
  9. Problem of Battery Network Management
  10. Problem Reformulation as Distributed MPC
  11. Numerical Results
  12. Conclusion

Key Result

Lemma 1

lu2024distributed The edge agreements problem_interest:edge are equivalent to the following equation: where $\bar{\boldsymbol{P}}$, $\bar{\boldsymbol{b}}$, and $\bar{\boldsymbol{H}}$ are as defined in eq:diag_mat_define, eq:edge_b_define, and eq:H_bar_define, respectively.

Figures (5)

  • Figure 1: The network communication topology.
  • Figure 2: A trajectory of $W_{1,k}$ and $W_{2,k}$ over iteration $k$ in log scale.
  • Figure 3: A trajectory of $\boldsymbol{f}(\boldsymbol{x}_k)$ and $\boldsymbol{x}^*$ over iteration $k$.
  • Figure 4: Communication topology of a LiBESS network
  • Figure 5: Simulation results of the LiBESS network.

Theorems & Definitions (14)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Lemma 2
  • proof
  • Theorem 1
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • ...and 4 more