Multi-objective optimal control with carbon emission and temperature constraints: for achieving a low-fossil-fuel economy
Central European Journal of Operations Research
In this paper, we propose a multi-objective control framework to address climate change, climate risks, and the transition to a low-carbon economy. Extending our previous collaborative work in Atolia et al. (Mathematical Control and Related Fields, 13:583–604, 2023), we build on a Nordhaus-type DICE model to incorporate optimal macroeconomic policies such as mitigation, adaptation, and climate-related infrastructure investment, with a focus on the dynamics of decarbonization. Based on a finite-horizon model that includes the threats of climate disasters arising from CO₂ emissions and temperature increases, we study preventive measures such as adaptation aimed at reducing disaster impacts. Our optimal control problem includes a dynamical system with a multi-dimensional state vector representing private capital, green capital, public capital, the stock of brown energy in the ground, carbon emissions, and temperature. The objective function captures preferences over consumption while also accounting for atmospheric CO₂, climate-risk events, and mitigation and adaptation policies. Given the multiple objectives involved in climate policy, the control vector includes mitigation, adaptation, and infrastructure investment decisions. The optimal control problem is studied under various state constraints. In two scenarios, we compute the Pareto front for a bi-objective control problem. Optimization over the Pareto front provides suitable weights for the two objectives. In particular, we explore the role of CO₂ constraints, as suggested by the Kyoto Protocol, and temperature constraints, as proposed in the Copenhagen and Paris agreements.