Optimal Control: Linear Quadratic Regulation

This lecture introduces the concept of linear quadratic regulation (LQR) in the context of optimal control for linear systems. The instructor explains how LQR aims to minimize a quadratic cost function to move the system state towards zero, by designing a controller that balances input energy and output energy. The lecture covers the formulation of the cost function, the selection of weighting matrices, and the implications of tuning the cost parameters. The instructor also discusses the stability of optimal solutions and the practical advantages of using LQR in complex, multi-input systems. The lecture concludes by highlighting the simplicity and effectiveness of LQR in real-world applications.