Variational Methods and Optimal Control III
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| Lecture 01 | ![slides [PDF]](images/slides.jpg) |
![notes [PDF]links](images/notes.jpg) |
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Introduction: motivation and revision | |
| Lecture 02 | |
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revision (extrema of surfaces, Taylor's theorem, the chain rule, ...) | |
| Lecture 03 | |
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revision (constrained extrema and Lagrange multipliers) | |
| Lecture 04 | |
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The 1st Variation: Euler-Lagrange formulation of the fixed end-point problem | |
| Lecture 05 | |
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autonomous problems: the catenary | |
| Lecture 06 | |
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autonomous problems: the brachystochrone | |
| Lecture 07 | |
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geodesics | |
| Lecture 08 | |
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invariance of the E-L equations, and degenerate equations | |
| Lecture 09 | |
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extensions: higher-order derivatives | |
| Lecture 10 | |
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extensions: several dependent variables | |
| Lecture 11 | |
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extensions: several independent variables | |
| Lecture 12 | |
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Numerical solutions | |
| Lecture 13 | |
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Numerical solutions continued | |
| Lecture 14 | |
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Constraints: integral constraints | |
| Lecture 15 | |
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integral constraints and Dido's problem | |
| Lecture 16 | |
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non-integral constraints and intro to optimal control | |
| Lecture 17 | |
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Free end points and natural boundary conditions | |
| Lecture 18 | |
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free and movable end points | |
| Lecture 19 | |
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transversals | |
| Lecture 20 | |
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broken extremals and corner conditions | |
| Lecture 21 | |
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Inequality constraints and optimal control | |
| Lecture 22 | |
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optimal control examples: planned growth | |
| Lecture 23 | |
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optimal control example: rocket launch profile | |
| Lecture 24 | |
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Hamilton's formulation | |
| Lecture 25 | |
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conservation laws and Noether's theorem | |
| Lecture 26 | |
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Pontryagin Maximum Principle and modern optimal control theory | |
| Lecture 27 | |
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bang-bang controllers | |
| Lecture 28 | |
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feedback controllers | |
| Lecture 29 | |
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Classification of extrema | |
| Lecture 30 | |
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revision |
Matthew Roughan
Last modified: Thu Apr 14 14:44:19 2016