Control systems are employed in vehicles, power plants, smart buildings, etc. Optimal control achieves the best performance in the presence of constraints. This is, for example, the case of airplanes, which optimize fuel consumption while obeying safety and comfort criteria. The chapter introduces basic concepts of control theory, focusing on the state variable approach, and then introduces important methods of optimal control, like the bang-bang control, the linear quadratic control, and the Kalman filter. This chapter contributes to motivating some matters of the following chapters. The optimal control study is facilitated by some specific functions of MATLAB, as it is shown in the included programs.