This paper presents a sensorless control to regulate the output voltage of a buck-boost converter that feeds an unknown DC load current. The proposed control is based on an inverse optimal control (IOC) theory, which computes the control action, minimizing a cost function associated with system variables. The IOC approach is an attractive technique, as it can be easily implemented without needing a direct solution of the Hamilton-Jacobi-Bellman (HJB) equation, which can be very complex. Furthermore, the proposed control includes a disturbance observer (DO) to estimate the DC load current, avoiding using a sensor. The DO method guarantees exponential convergence to the estimated variable, regardless of the initial estimation points. Time-dominated simulations are examined to evaluate the proposed control's performance while regulating a Buck-Boost converter's output voltage. These simulations were carried out in the PLECS software (MATLAB/Simulink simulation environment). Additionally, the simulation results show the robustness and effectiveness of the proposed sensorless IOC approach when compared to sliding mode control.