Linear Quadractic Regulator LQR
Linear Quadratic Regulators work by finding trade-off that drives our system to its desired setpoint while using the minumum control effort. For example, a spaceship might want to minimize the fuel it expends to reach a given reference, while a high-speed robotic arm might need to react quickly to disturbances and reach the setpoint quickly.
Watch this LQR video for a good explaination of the Linear Quadratic Regulators.
References
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FRC Documentation Linear Quadratic Regulator
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Tyler Veness Controls Engineering in the FIRST Robotics Competition Chapter 6.9.
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Christopher Lum Introduction to Linear Quadratic Regulator (LQR) Control