TY - EJOU
AU - Liu, Cheinshan
AU - Kuo, Chunglun
AU - Chang, Jiangren
TI - Solving the Optimal Control Problems of Nonlinear Duffing Oscillators By Using an Iterative Shape Functions Method
T2 - Computer Modeling in Engineering \& Sciences
PY - 2020
VL - 122
IS - 1
SN - 1526-1506
AB - 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.
KW - Nonlinear Duffing oscillator
KW - optimal control problem
KW - Hamiltonian formulation
KW - shape functions method
KW - iterative algorithm
DO - 10.32604/cmes.2020.08490