QA116 : An application of collocation method for solving time-delayed optimal control problems
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2012
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Abstarct: In this thesis, we solve a class of time-delayed optimal control problems using Haar
wavelets. In the first chapter, we introduce general optimal control problems, Haar
wavelets and express the needed definitions and theorems. In the second chapter, we
study Bolza optimal control problems with time-delayed. The problem is first transformed, using a Pade approximation, to one without a time-delayed argument. Then
we approximate it using Haar wavelets. Numerical results are also given for four test
examples. The third chapter consists of infinite-horizon time-delayed optimal control
problem. The problem is first transformed, using a Pade approximation, to one without a time-delayed argument. Then by a suitable change of variable, we transformed
the obtained non-delay optimal control problem to a finite-horizon optimal control
problem. We solve it numerically using Haar wavelets. In fourth chapter, we express
nonlinear optimal control problems with external disturbances and control delay. Using Artstein transformation, the problem is translated into simple nonlinear problem
without delay. Then it is approximated by Haar wavelet. Numerical results are also
given for one test examples to demonstrate the applicability and the efficiency of the
method. In the fifth chapter, we consider the immune Response as an optimal control
problem with time-delays. Similar to the second chapter, the problem is transformed
into non-delay problem. Then it is approximated using Haar wavelet. In this thesis
all graphs are plotted by matlab software.
Keywords:
#Haar wavelets #Rationalized Haar functions #Páde approximation #Time-delayed optimal control problems #Infinite-horizon problems #Artstein transformation #Collocation points #Nonlinear optimal control problem with external disturbances #Immune Response Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
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