A Differential Game-Based Minimax Control Strategy for Multi-Agent Energy Management In Smart Microgrids

Abstract

The growing penetration of distributed energy resources, electric vehicles, and controllable loads is making smart microgrids tightly coupled multi-agent systems that must deliver reliable performance while facing ongoing renewable and demand uncertainties. Traditional approaches that rely on optimization methods or single-agent controllers cannot ensure robust performance when several agents act independently according to their rational strategies, especially in the face of adverse disturbances such as renewable production outages, load increases, or communication delays in the common network. In this paper, a decisive game-theoretic minimax control idea is introduced to describe multi-agent energy management in terms of a dynamic zero-sum game established between the coordinating controller and the worst-case disturbance to be solved by implementing feedback saddle-point policy derived from Hamilton-Jacobi-Isaacs value function. Each agent, including distributed generators, energy storage systems, electric vehicles aggregators and controllable loads update its state dynamics through communication bus and the minimax controller calculates robust control gains as far as the worst disturbance is allowed. The developed approach was tested in MATLAB/Simulink co-simulation environment based on 24-hour synthetic microgrid scenarios with 48 loads, photovoltaic generation and price samples. The performance of the proposed decision-making approach is better than feedback Nash game, model predictive control and rule-based heuristics as it has resulted in 23.6% decrease in average operating costs, 61.4% decrease in the frequency deviations, 78.2% decrease in state-of-charge violations and 47.5% faster calculations of value function yielding 0.91 minimum robustness index compared to the 0.42-0.74 for baseline algorithm. The ablation study demonstrated that 14.8% improvement of operating cost index is provided by the introduction of the worst-case disturbance concept. These results indicate that embedding a minimax differential game formulation into multi agent microgrid control yields measurable robustness and economic gains over cooperative and predictive alternatives, providing a practical pathway toward resilient, decentralized energy management architectures.