Week 11
LQR and Cost Functions
I use the saved simulation video as a starting point to revisit state-space control, observers, and digital control.
What I connect in this unit
LQR penalizes state deviation and input effort together in a quadratic cost. Q and R weights set the state-input trade-off, and the Riccati equation yields feedback gain without directly prescribing every pole.
Concept map
- Quadratic cost
- Q and R weights
- Riccati equation
- State-input trade-off
Technical anchor
Write J=∫(x^TQx+u^TRu)dt and obtain K=R^-1 B^T P from the Riccati solution P. Vary one diagonal weight in Q or R and compare the resulting poles and u(t).
How I review it
Avoid weights that ignore state units by comparing Q before and after normalization; then check peak input and each state's settling in addition to stability.
Connection to the full course
Unit 11 of 12. This study sequence connects the system flow visible in the video with standard control topics; it is not a claim about lecture weeks.