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A Distributed Time-Varying Optimization Approach Based on an Event-Triggered Scheme

Haojin Li, Xiaodong Cheng, Peter van Heijster, Sitian Qin

Abstract

In this paper, we present an event-triggered distributed optimization approach including a distributed controller to solve a class of distributed time-varying optimization problems (DTOP). The proposed approach is developed within a distributed neurodynamic (DND) framework that not only optimizes the global objective function in real-time, but also ensures that the states of the agents converge to consensus. This work stands out from existing methods in two key aspects. First, the distributed controller enables the agents to communicate only at designed instants rather than continuously by an event-triggered scheme, which reduces the energy required for agent communication. Second, by incorporating an integral mode technique, the event-triggered distributed controller avoids computing the inverse of the Hessian of each local objective function, thereby reducing computational costs. Finally, an example of battery charging problem is provided to demonstrate the effectiveness of the proposed event-triggered distributed optimization approach.

A Distributed Time-Varying Optimization Approach Based on an Event-Triggered Scheme

Abstract

In this paper, we present an event-triggered distributed optimization approach including a distributed controller to solve a class of distributed time-varying optimization problems (DTOP). The proposed approach is developed within a distributed neurodynamic (DND) framework that not only optimizes the global objective function in real-time, but also ensures that the states of the agents converge to consensus. This work stands out from existing methods in two key aspects. First, the distributed controller enables the agents to communicate only at designed instants rather than continuously by an event-triggered scheme, which reduces the energy required for agent communication. Second, by incorporating an integral mode technique, the event-triggered distributed controller avoids computing the inverse of the Hessian of each local objective function, thereby reducing computational costs. Finally, an example of battery charging problem is provided to demonstrate the effectiveness of the proposed event-triggered distributed optimization approach.

Paper Structure

This paper contains 8 sections, 4 theorems, 31 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Graph Theory
  5. Problem Description
  6. Main Results
  7. Numerical Simulation
  8. Conclusion

Key Result

Theorem 3.1

Consider the distributed controller controller with the event-triggered scheme trigger_scheme for each agent $i$. Under Assumptions as3-as2, if then the state of each agent $x_i$ reaches consensus and cooperatively track the optimal trajectory $x^*(t)$ of the DTOP DTOP. Furthermore, the Zeno behavior is excluded.

Figures (6)

  • Figure 1: Block diagram of the proposed event-triggered DND approach.
  • Figure 2: The communication graph among battery packages.
  • Figure 3: Trajectories of power output.
  • Figure 4: The errors between $P_i$ and $P^*$.
  • Figure 5: The triggering instants of each battery package. (a) The communication instants triggered in the full interval $t\in[0, 6]$. (b) Zoomed-in figure showing the communication instants in the region $t\in[5.4, 6]$ (boxed area in (a)).
  • ...and 1 more figures

Theorems & Definitions (7)

  • Remark 1
  • Remark 2
  • Theorem 3.1
  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • Remark 3