Multi-objective optimal control with carbon emission and temperature constraints: for achieving a low-fossil-fuel economy

Abstract In this paper we propose multi-objective control to deal with climate change and climate risks and the transition to a low carbon economy. Extending our previous collaborative work as in Atolia et al. (Math Control Related Fields, 13:583–604, 2023), we again build on the Nordhaus type DICE model to include various optimal macroeconomic policies such as mitigation, adaptation and climate-related infrastructure investment studying the dynamics of the decarbonizing of the economy. Based on a finite horizon model that includes the threats of climate disasters arising from $$CO_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> emissions and temperature rise, we deal with preventive measures such as adaptation reducing disaster effects. Our optimal control problem of finite horizon is consisting of a dynamical system with five-dimensional state vector representing stocks of private capital, green capital, public capital, stock of brown energy in the ground, carbon emissions, and temperature. The objective function captures preferences over consumption but is also impacted by atmospheric $$CO_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> , climate risks events and by mitigation and adaptation policies. Given the numerous challenges to climate change policies with multiple objectives the control vector is eight-dimensional including mitigation, adaptation and infrastructure investment. 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 us with suitable weights for the two objectives. In particular we explore the role of $$CO_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> constraints, as the Kyoto Protocol has suggested, and temperature constraints, as the Copenhagen–Paris agreements have proposed.