Linear Quadratic Regulator

This chapter presents how optimal control is used in the form of feedback so that optimal control can be implemented on real systems. We consider linear plants and quadratic cost functions and develop the optimal regulator, which is known as the linear quadratic regulator (LQR). The nature of the optimality under LQR is analyzed, and the finite-time and infinite-time regulation processes are presented. Finally, the performance of LQR and PID control systems is compared.