@Article{cmes.2020.08490,
AUTHOR = {Cheinshan Liu, Chunglun Kuo, Jiangren Chang},
TITLE = {Solving the Optimal Control Problems of Nonlinear Duffing Oscillators By Using an Iterative Shape Functions Method},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {122},
YEAR = {2020},
NUMBER = {1},
PAGES = {33--48},
URL = {http://www.techscience.com/CMES/v122n1/38234},
ISSN = {1526-1506},
ABSTRACT = {In the optimal control problem of nonlinear dynamical system, the 
Hamiltonian formulation is useful and powerful to solve an optimal control force. 
However, the resulting Euler-Lagrange equations are not easy to solve, when the 
performance index is complicated, because one may encounter a two-point boundary 
value problem of nonlinear differential algebraic equations. To be a numerical method, it 
is hard to exactly preserve all the specified conditions, which might deteriorate the 
accuracy of numerical solution. With this in mind, we develop a novel algorithm to find 
the solution of the optimal control problem of nonlinear Duffing oscillator, which can 
exactly satisfy all the required conditions for the minimality of the performance index. A 
new idea of shape functions method (SFM) is introduced, from which we can transform 
the optimal control problems to the initial value problems for the new variables, whose 
initial values are given arbitrarily, and meanwhile the terminal values are determined 
iteratively. Numerical examples confirm the high-performance of the iterative algorithms 
based on the SFM, which are convergence fast, and also provide very accurate solutions.
The new algorithm is robust, even large noise is imposed on the input data.},
DOI = {10.32604/cmes.2020.08490}
}