Linear Quadratic Regulator (LQR)

The Linear Quadratic Regulator (LQR) is a mathematical method used in control theory to design a system that optimally manages behavior over time. It balances two goals: maintaining system performance (like stability) and minimizing costs (like energy use or deviations from a desired state). LQR does this by choosing the best control actions based on a linear model of the system while using a quadratic cost function to penalize undesirable outcomes. Essentially, it helps ensure systems behave as desired while efficiently managing resources. Common applications include robotics, aerospace, and economics.