Linear Quadratic (LQ) Optimal Control: Proof of Theorem

This lecture covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon. It explains the solution to the FH-LQ problem, the stability of the closed-loop system, and the state-feedback regulator. The lecture also delves into the minimization of quadratic forms and the dynamic programming argument used in the computation of the cost-to-go. The Difference Riccati Equation (DRE) and the backward iterations for computing the optimal control law are discussed in detail.