Keywords
LQR = linear-quadratic regulator
LQG = linear-quadratic Gaussian
HJB = Hamilton-Jacobi-Bellman
| Lec # | Topics | Notes |
|---|---|---|
| 1 | Nonlinear optimization: unconstrained nonlinear optimization, line search methods | (PDF - 1.9 MB) |
| 2 |
Nonlinear optimization: constrained nonlinear optimization, Lagrange multipliers Penalty/barrier functions are also often used, but will not be discussed here. | (PDF - 1.2 MB) |
| 3 | Dynamic programming: principle of optimality, dynamic programming, discrete LQR | (PDF - 1.0 MB) |
| 4 | HJB equation: differential pressure in continuous time, HJB equation, continuous LQR | (PDF) |
| 5 |
Calculus of variations Most books cover this material well, but Kirk (chapter 4) does a particularly nice job. See here for an online reference. | (PDF) |
| 6 | Calculus of variations applied to optimal control | (PDF) |
| 7 | Numerical solution in MATLAB | (PDF) |
| 8 |
Properties of optimal control solution Bryson and Ho, Section 3.5 and Kirk, Section 4.4 | (PDF) |
| 9 |
Constrained optimal control Bryson and Ho, section 3.x and Kirk, section 5.3 | (PDF) |
| 10 |
Singular arcs Bryson, chapter 8 and Kirk, section 5.6 | (PDF) |
| 11 |
Estimators/Observers Bryson, chapter 12 and Gelb, Optimal Estimation | (PDF) |
| 12 |
Stochastic optimal control Kwaknernaak and Sivan, chapters 3.6, 5; Bryson, chapter 14; and Stengel, chapter 5 | (PDF) |
| 13 |
LQG robustness Stengel, chapter 6 Question: how well do the large gain and phase margins discussed for LQR (6-29) map over to LQG? | (PDF) |
| 14 | 16.31 Feedback Control Systems: multiple-input multiple-output (MIMO) systems, singular value decomposition | (PDF) |
| 15 | Signals and system norms: H∞ synthesis, different type of optimal controller | (PDF) |
| 16 | Model predictive control | (PDF) |