Prescribed-Time Convergent Distributed Multiobjective Optimization With Dynamic Event-Triggered Communication

TL;DR

This work tackles distributed constrained multiobjective resource allocation in multi-agent networks by recasting multiple local objectives into a single objective via a distributed weighted $L_p$ preference, enabling fully decentralized optimization under both local and global constraints. A novel algorithm combines prescribed-time control with dynamic ETMs and generalized time-based generators to achieve convergence within user-defined horizons while minimizing communication and avoiding Zeno behavior. Theoretical guarantees are provided through Lyapunov analysis, showing prescribed-time convergence to optimality and KKT-consistent equilibria, alongside online weight adaptation and ideal-point computation. Simulation on an IEEE 14-bus microgrid demonstrates flexible TBG configurations, reduced communications, and robust performance, highlighting practical applicability to energy systems and distributed robotics. Overall, the approach advances distributed multiobjective optimization by offering a flexible, efficient, and provably convergent framework for constrained resource allocation without centralized coordination.

Abstract

This paper addresses distributed constrained multiobjective resource allocation problems (DCMRAPs) in multi-agent networks, where agents face multiple conflicting local objectives under local and global constraints. By reformulating DCMRAPs as single-objective weighted $L_p$ problems, the proposed approach enables distributed solutions without relying on predefined weighting coefficients or centralized decision-making. Leveraging prescribed-time control and dynamic event-triggered mechanisms (ETMs), a novel distributed algorithm is proposed within a prescribed time through sampled communication. Using generalized time-based generators (TBGs), the algorithm provides more flexibility in optimizing solution accuracy and trajectory smoothness without the constraints of initial conditions. Novel dynamic ETMs, integrated with generalized TBGs, improve communication efficiency by adapting to local error metrics and network-based disagreements, while providing enhanced flexibility in balancing solution accuracy and communication frequency. The Zeno behavior is excluded. Validated by Lyapunov analysis and simulation experiments, our method demonstrates superior control performance and efficiency compared to existing methods, advancing distributed optimization across diverse applications.

Figures (6)

• Figure 1: IEEE 14-bus system with communication network.
• Figure 2: Power outputs and communications of $u_i$ using the proposed algorithm (\ref{['solutionforsubproblem']})-(\ref{['dynamicETM2']}) with different TBGs. (a) TBG 1 (\ref{['TBG1']}) with $t_{\rm pre 1} =t_{\rm pre 2}= 2$, $t_{\rm pre 3} = 3$; (b) TBG 1 (\ref{['TBG1']}) with $t_{\rm pre 1} =t_{\rm pre 2}= 1$, $t_{\rm pre 3} = 2$; (c) TBG 2 (\ref{['TBG2']}) with $t_{\rm pre 1} =t_{\rm pre 2}= 2$, $t_{\rm pre 3} = 3$; (d) TBG 3 (\ref{['TBG3']}) with $t_{\rm pre 1} =t_{\rm pre 2}= 2$, $t_{\rm pre 3} = 3$.
• Figure 3: Evolution of weighting coefficients in Case 1.
• Figure 4: Simulation results using different TBGs (\ref{['TBG1']})-(\ref{['TBG3']}). (a) Outputs of TBGs; (b) Imbalance between demand and supply $\sum_{i=1}^{N}(1+\varrho_i)P_{d,i} - P_i$.
• Figure 5: Dynamic evolution of (a) Exchanged information $\bar{\nu}_i$; (b) Internal dynamic variables $\eta_i$.

Theorems & Definitions (22)

• Lemma 1: Orthogonal Transformation yi2018doubleorder
• Definition 1: Strong Convexity
• Lemma 2: ruszczynski2011nonlinear
• Definition 2: Normal Cone and Tangent Cone ruszczynski2011nonlinear
• Lemma 3: BROGLIATO2006ontheequivalenceyi2016initialization
• Definition 3: liu2023multiobjective
• Lemma 4: liu2023multiobjective
• Lemma 5
• Remark 1
• Remark 2