A cell-averaging Chebyshev spectral method for the controlled Duffing oscillator Original Research Article

In order to maintain spectral accuracy, the grids on which a physical problem is to be solved must also be obtained by spectrally accurate techniques. This paper presents a spectral method of solving the controlled Duffing oscillator. The method is based upon constructing the Mth-degree interpolation polynomials, using Chebyshev nodes, to approximate the state and the control vectors. The differential and integral expressions which arise from the system dynamics and the performance index are converted into an algebraic nonlinear programming problem. The results of computer simulation studies compare favorably to optimal solutions obtained by closed-form analysis and/or by other numerical schemes.