A Linear Quadratic Regulator (LQR) is a mathematical method used in control theory to design a controller that regulates the behavior of dynamic systems. It aims to minimize a cost function, which typically includes terms for the state of the system and the control effort. By balancing these factors, LQR provides an optimal control strategy that ensures stability and performance. LQR is particularly useful for systems that can be modeled with linear equations and where the performance can be quantified using quadratic cost functions. It is widely applied in various fields, including robotics, aerospace, and automotive engineering, to achieve efficient and effective control.