LQR (Linear Quadratic Regulator)

The Linear Quadratic Regulator (LQR) is a control system technique used to guide a system toward desired behavior efficiently. It models the system's dynamics with linear equations and determines the optimal way to control it by minimizing a cost function that balances performance (like accuracy) and effort (like energy used). Essentially, LQR computes the best control actions to keep the system stable and responsive, ensuring it reaches its goals smoothly while avoiding excessive inputs. It’s widely used in engineering for optimal control of robots, vehicles, and other dynamic systems.