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Numerical solution of the controlled Duffing oscillator by the pseudospectral method. (English) Zbl 0827.65074
The authors introduce a new direct numerical method for solving the controlled Duffing oscillator. The method is based on a pseudospectral method in which the authors construct the \(m\)th degree interpolation polynomials using the Legendre-Gauss-Lobatto collocation points to approximate the state and control functions.
With this method, the system dynamics, initial conditions and the integral expression are converted to a system of algebraic equations that can be solved for the unknown coefficients by the iterative Newton method. Finally, numerical results are presented and a comparison is made with an existing method of Chebyshev approximation to demonstrate the efficiency and the accuracy of the proposed numerical method.

MSC:
65K10 Numerical optimization and variational techniques
93C15 Control/observation systems governed by ordinary differential equations
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