Optimal Control for Sustainable Intervention in a Coupled Socio-Climatic Model of Air Pollution

Abstract

In this paper, technological interventions in a simple airshed model of emission propagation coupled with a social model of technology adoption are studied. An optimal control problem is introduced where a central planner aims to balance pollution concentration against intervention costs over an infinite time horizon. Interventions are classified into two types. Preventive interventions promote the adoption of low emission (green) technologies in the underlying population whereas dissipative interventions reduce the concentration of pre-existing pollutants in the air. Next, an infinite-horizon optimal control problem is set up and the notion of optimality is established. Applying Pontryagin's Minimum Principle, a sustainable equilibrium is derived and the existence of its stable manifold is explored. Imposition of green technology reduces both the steady-state pollutant concentration and dissipative Effort simultaneously but the planning variables induce a tradeoff between concentration and dissipative Effort. Lastly, the stable manifolds are simulated concluding with a discussion on policy implications for the system under consideration.