Model Predictive Control for Coupled Adoption-Opinion Dynamics

Abstract: This paper investigates an optimal control problem for an adoption-opinion model that couples opinion dynamics with a compartmental adoption framework on a multilayer network to study the diffusion of sustainable behaviors. Adoption evolves through social contagion and perceived benefits, while opinions are shaped by social interactions and feedback from adoption levels. Individuals may also stop adopting virtuous behavior due to external constraints or shifting perceptions, affecting overall diffusion. After the stability analysis of equilibria, both in the presence and absence of adopters, we introduce a Model Predictive Control (MPC) framework that optimizes interventions by shaping opinions rather than directly enforcing adoption. This nudge-based control strategy allows policymakers to influence diffusion indirectly, making interventions more effective and scalable. Numerical simulations demonstrate that, in the absence of control, adoption stagnates, whereas MPC-driven interventions sustain and enhance adoption across communities.