Variational Methods and Optimal Control III
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Description
Many problems of optimisation and control in the sciences and engineering seek to find the shape of a curve or surface satisfying certain conditions so as to maximise or minimise some quantity. For example, shape a yacht hull so as to minimise fluid drag. Variational methods involve an extension of calculus techniques to handle such problems. This course develops an appropriate methodology, illustrated by a variety of physical and engineering problems.
Objective
Content
Topics covered are: Classical Calculus of Variations problems such as calculation of the shape of geodesics, the Cantenary, and the Brachystochrone; the derivation and use of the simpler Euler-Lagrange equations for second-order (the Euler-Poisson equation), multiple dependent variables (Hamilton's equations), and multiple independent variables (minimal surfaces); constrained problems and problems with non-integral constraints; Euler's finite differences, Ritz's method and Kantorich's method; conservation laws and Noether's theorem; classification of extremals using second variation; optimal control via the Pontryagin Maximum Principle, and its applications to space-flight calculations.
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| Year |
Semester |
Level |
Units |
| 2013 |
2 |
3 |
3 |
Delivery
36 hours of lectures and tutorials
Assessment
Ongoing assessment 30%, exam 70%.
Graduate attributes
Linkage past
No past linkages have been noted.
Linkage present
No present linkages have been noted.
Linkage future
This course is not recorded as prequisite for other courses.
Restrictions
None.
Recommended text
None.
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