Solar systems' outlet temperature plays a key role in the sustainability of power generation in solar-assisted power plants. Increasing this temperature to its maximum possible level would increase the contribution of solar energy to power generation. Control systems are meant to maintain this temperature at a desired level by adjusting the mass flow rate circulating in the solar unit. The designed controller for the plant can directly affect the expenses associated with the solar unit since the system can respond significantly faster to different working loads. This paper attempts to reduce the operating time of a combined power plant using a non-linear control system. Along with applying a control system to the plant, an exergoeconomic analysis is also performed to obtain the expenses of various fluid flow streams of the plant while occupying it with a controller. Energy and exergy analyses are also carried out to evaluate the thermal and exergetic efficiencies of the studied plant. After obtaining the solar unit's operating time, efficiencies, and expenses associated with the carbon capture and power generation, an optimum working condition for the plant is determined. Multi-objective optimization using the particle swarm optimization (PSO) algorithm is run to minimize the system's operating time and costs and to maximize efficiencies. Results indicate that the optimal power plant can get as much as 51.61%, 29.79%, 6.27 ($/Gj), 226.73 ($/Gj), and 25.57 (min) for exergy efficiencies, energy efficiencies, power production, carbon capture costs, and solar system operation time, respectively.