Multi-Agent Cooperative Optimisation of Microwave Heating Based on Phase–Power Coordinated Control and Consensus Feedback

To address the key challenges of non-uniform energy distribution, local overheating, and unstable electromagnetic–thermal coupling in multi-source microwave heating systems, this paper proposes a distributed optimisation cooperative method based on phase–power coordinated control and consensus-feedback constraints. A two-stage multi-agent control mechanism, described as “phase leading, power following”, is constructed within a hierarchical architecture to achieve spatiotemporal collaborative optimisation from the perspectives of electromagnetic interference-field shaping and thermal feedback regulation. In the phase-regulation stage (Innovation 1), adaptive reconstruction of the interference field is achieved through relative phase specification and a two-level scanning mechanism, rapidly shaping the spatial energy distribution and enhancing the absorption efficiency of incident electromagnetic energy in the cavity–material system. In the power-regulation stage (Innovation 2), amplitude correction is performed under a stabilised interference-field background, and a consensus-feedback constrained regional energy collaboration network is established to ensure that regional energy states converge within the convex hull of the leader reference set. Power redistribution is driven by the target–region energy deviation and neighbourhood consistency relationships, enabling spatial reverse balancing of energy density, suppressing excessive heating in high-energy regions, and enhancing compensation in low-energy regions. Furthermore, a spatiotemporal dual-scale coupling consensus-optimisation framework (Innovation 3) is developed to form a cooperative loop between fast electromagnetic-field reconstruction and slow thermal-field dynamics, achieving synchronous improvement in energy utilisation efficiency and temperature-field uniformity with stable convergence. Simulation results demonstrate that, compared with conventional constant-power, single-phase, and single-power control strategies, the proposed method improves heating efficiency by 16.62–44.74%, and enhances temperature uniformity in vertical and horizontal sections by 8.84–55.87% and 11.41–40.54%, respectively.