By Using the Lie-group Shooting Method to Solve the Optimal Control Problems of Nonlinear Duffing Oscillators
Date Issued
2015
Date
2015
Author(s)
Liu, Tzu-Min
Abstract
In the optimal control theory, the Hamiltonian formulation is a famous one which is convenient to find an optimally designed control force. However, when the performance index is a complicated function of control force, the Hamiltonian method is not easy to find the optimal closed-form solution, because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations (DAEs). In this thesis, we address this issue via an novel approach, of which the optimal vibration control problem of Duffing oscillator is recast into a two-point nonlinear DAEs. We develop the corresponding and shooting methods, as well as a Lie-group differential algebraic equations (LGDAE) method to numerically solve the optimal control problems of nonlinear Duffing oscillators. Seven examples of a single Duffing oscillator and one coupled Duffing oscillators are used to test the performance of the present method.
Subjects
Duffing oscillator
Optimal control problem
Hamiltonian formulation
Lie-group method
Lie-group shooting method
Lie-group differential algebraic equations method
Type
thesis
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