Title:
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Numerical techniques for singular optimal trajectories.
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The objectives of the subject-matter of this
thesis were to appraise some methods of solving
non-singular optimal control problems by their degree
of success in tackling four chosen problems and then to
try the most promising methods on chosen singular
problems.
In Part I of this thesis, the chosen problems are
attempted by quasilinearisation, two versions of
shooting, Miels's method, differential dynamic
programming and two versions of parameterisation .
Conclusions on the various methods are given. NOC
shooting, developed by the Numerical Optimisation
Centre of The Hatfield Polytechnic, and constrained
optimisation were found to be very useful for
non-singular problems.
In Part 11, the properties and calculation of
possible singular controls are investigated, then the
two chosen methods used. It was found that NOC
shooting was again very useful, provided the solution
structure is known and that constrained
parameterisation was invaluable for determining the
solution structure and when shooting is impossible.
Contributions to knowledge as as follows. In
Part I, the relative merits of various methods are
displayed, additions are made to the theory of parameterisation, shooting and quasilinearisation, the best solutions known of the chosen problems are produced and choices of optimisation parameters for one chosen problem, the satellite problem, are compared. The satellite problem has dependent state variables and the Maximum Principle is extended in
Appendix III to cover this case . In Part II, a
thorough survey of the properties of singular
controls is given, the calculation of possible
singular controls clarified and extended, the utility
of the two chosen methods is displayed, the best
solutions known of the Goddard problem obtained with
improved understanding of transitions in soluti on
structures , Cl problem studied with control dependent
on the costate variables and singular solution
structures found.
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