Linear Quadratic Optimal Control: Analysis and Solution

This lecture covers Linear Quadratic (LQ) optimal control over a finite horizon, including the definition of the problem, analysis of the cost, and the recursive formula for the optimal gains. It delves into the Difference Riccati Equation and the properties of Q, S, R matrices. The solution to the FH-LQ problem is presented, discussing the unique control law, the computation of control gains, and the Difference Riccati Equation. The stability of the closed-loop system and the proof of the theorem regarding the minimization of quadratic forms are also explained.