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DOI: 10.23952/cot.2025.46
Received June 24, 2024; Accepted October 26, 2024; Published online October 11, 2025
Abstract. We study a CO2 emissions control problem with smooth seasonal fluctuations of the CO2 reduction rate due to photosynthesis, where the dynamics of a state variable is generated by a non-autonomous ordinary differential equation. The current value Hamiltonian of the problem is linear in the state variable, and so the dynamics of its co-state variable is de-coupled from that of the state variable. We show that the co-state variable exhibits periodic oscillations, that a unique nontrivial optimal solution does exists under some additional inequality constraint, and that under this constraint the state variable converges to a non-autonomous limit cycle globally on the unique optimal path that exhibits the turnpike property.
How to Cite this Article:
S. Asaoka, K. Nishimura, T. Shigoka, M. Yano, On the optimal non-autonomous limit cycle in the CO2 emissions control problem with smooth seasonal fluctuations, Commun. Optim. Theory 2025 (2025) 46.