**Sergei A. Soldatenko**

St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences, No. 39, 14-th Line, St. Petersburg 199178, Russia; soldatenko@iias.spb.su; Tel.: +7-931-354-0598

Received: 28 September 2018; Accepted: 26 October 2018; Published: 28 October 2018

**Abstract:** In this paper, we apply the optimal control theory to obtain the analytic solutions of the two-component globally averaged energy balance model in order to estimate the influence of solar radiation management (SRM) operations on the global mean surface temperature in the 21st century. It is assumed that SRM is executed via injection of sulfur aerosols into the stratosphere to limit the global temperature increase in the year 2100 by 1.5 ◦C and keeping global temperature over the specified period (2020–2100) within 2 ◦C as required by the Paris climate agreement. The radiative forcing produced by the rise in the atmospheric concentrations of greenhouse gases is defined by the Representative Concentration Pathways and the 1pctCO2 (1% per year CO2 increase) scenario. The goal of SRM is formulated in terms of extremal problem, which entails finding a control function (the albedo of aerosol layer) that minimizes the amount of aerosols injected into the upper atmosphere to satisfy the Paris climate target. For each climate change scenario, the optimal albedo of the aerosol layer and the corresponding global mean surface temperature changes were obtained. In addition, the aerosol emission rates required to create an aerosol cloud with optimal optical properties were calculated.

**Keywords:** climate change; optimal control; geoengineering; climate manipulation
