Observer-Based Adaptive Robust Control of Dual-Layer Multiagent Epidemic Model: Physical and Information Layers

This paper proposes an innovative dual-layer multi-agent-based SIS epidemic model, incorporating a physical contact layer to model disease spread through travel or migration between cities, and an information layer to enable the sharing of infection data among healthcare providers across cities even without direct physical connections. An observer is designed to estimate the infected fraction in each city, utilising estimates from neighbouring cities connected in the physical layer in a distributed manner; these estimates are then leveraged in the information layer to synchronise each city's infection trajectory with a virtual leader. Additionally, the control input, typically formulated in multi-agent systems (MAS), is adopted as the sliding surface, with its stability demonstrated via Lyapunov analysis within the dual-layer SIS framework. An adaptive sliding mode control (ASMC) strategy is developed to address parameter uncertainties to reach this sliding surface, effectively integrating the physical and information layers’ dynamics to drive cities toward disease eradication. Finally, a numerical example is provided to validate the accuracy of the theoretical results.