by Daniel Sinderson
This is course 2A in my DIY graduate program. It’s a year-long course in dynamical systems, differential equations, and optimal control theory.
| # | Chapter | HW | Lab |
|---|---|---|---|
| 1 | Modeling | Notes | |
| 2 | Existence and Uniqueness | Notes | Intro to IVP and BVP |
| 3 | Stability Theory | Notes | |
| 4 | Problem Sets | Modeling the Spread of an Epidemic: SIR Models | |
| 5 | Bifurcation Theory | Notes | |
| 6 | PDE Introduction | Notes | Predator-Prey Models |
| 7 | Hyperbolic PDE | Notes | |
| 8 | Auxiliary Conditions, Well-Posedness, and Parabolic and Elliptic equations | Notes | Bifurcations and Hysteresis |
| 9 | Eigenfunction Expansions | Notes | |
| 10 | Green’s Function | Notes | Wave Phenomena |
| 11 | Introduction to Optimization and the Calculus of Variations | Notes | |
| 12 | The Simplest Problem | Notes | Heat Flow |
| 13 | Generalizations of the Simplest Problem | Notes | |
| 14 | Constraints | Notes | Anisotropic Diffusion |
| 15 | Hamilton’s Principle | Notes | |
| 16 | Symmetry and Conservation: Noether’s Theorem | Notes | Poisson’s Equation |
| 17 | Necessary AND Sufficient Conditions for Weak Maxima/Minima | Notes | |
| 18 | Strong Extrema | Notes | Spectral 1: Method of Mean Weighted Residuals |
| 19 | Introduction to Optimal Control | Notes | |
| 20 | Formal Derivation of Pontraygin’s Maximum Principle | Notes | Spectral 2: A Pseudospectral Method for Periodic Functions |
| 21 | Bang-bang and singular control problems | Notes | |
| 22 | Different forms of the cost-functional | Notes | HIV Treatment Using Optimal Control |
| 23 | Linear Quadratic Regulator (the ‘right’ way to optimize) | Notes | |
| 24 | Inequality constraints | Notes | Solitons |
| 25 | Hamilton Jacobi Bellman Equation | Notes | |
| 26 | Mathematical Systems | Notes | Obstacle Avoidance |
| 27 | Control Theory: Discrete Case | Notes | |
| 28 | Linear Control Theory | Notes | The Inverted Pendulum |
| 29 | Optimal Control | Notes | |
| 30 | Problem Sets | LQG |
Written on: December 1, 2024