Distributed multi-objective optimization for discrete-time heterogeneous Multi-agent systems: A potential game-based...

This paper addresses the distributed multi-objective optimization problem for discrete-time heterogeneous multi-agent systems via potential games. Potential game-based methods are widely employed in distributed optimization for multi-agent systems, as they enable the decoupling of solution processes and ensure convergence to the desirable equilibrium. While potential game theory is effective for single-objective cases, its multi-objective extension lacks a systematic framework, is limited by strict assumptions, and exhibits poor explainability. To overcome these limitations, a novel semi-tensor product (STP)-based framework is proposed, which is one of the powerful tools for the research of finite potential games. The main contributions are (1) formulating a novel game model-finite multi-objective networked potential games (MONPGs)-for heterogeneous interactions, with an STP-based algebraic condition enabling local information-based payoff design; (2) designing a strategy learning algorithm that guarantees the convergence to a Pareto equilibrium and is universally applicable to arbitrary real-valued payoff vectors, significantly enhancing generality compared to prior works; and (3) deriving a sufficient condition expressed as a linear matrix equation for solving the distributed optimization problem. This work extends potential game-based methods to multi-objective and heterogeneous interaction settings, enhancing interpretability and solving a class of problems previously intractable for existing potential game-based methods.