Optimal control theory deals with finding a control law for a dynamical system over a given period of time such that an objective function is optimized. This chapter starts with an overview of the classical linear quadratic regulator (LQR). This is followed by introducing the general idea of dynamical programming and its specific application to help solve the LQR problem. Then, the LQR is presented when model uncertainty and observational noise appear. Kalman filter is incorporated into the standard LQR solver to find the solution. The chapter also includes the general optimal control framework. Simple examples are used to illustrate the use of the general theory for solving control problems. Statistical control is briefly mentioned at the end of this chapter.