Chebyshev series solution of the controlled Duffing oscillator

DOI10.1016/0021-9991(82)90085-7zbMath0493.65031OpenAlexW2032223816MaRDI QIDQ1168691

René van Dooren, Jacques Vlassenbroeck

Publication date: 1982

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(82)90085-7

zbMATH Keywords

Lagrange multipliersminimax principlesleast squares techniquesChebyshev series solutioncontrolled Duffing oscillatorNewton- Raphson iterative method

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Nonlinear systems in control theory (93C10) Control/observation systems governed by ordinary differential equations (93C15) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (16)

Numerical study of the controlled van der Pol oscillator in Chebyshev series ⋮ Numerical solution of the controlled Duffing oscillator by the pseudospectral method ⋮ A Chebyshev polynomial method for optimal control with state constraints ⋮ A cell-averaging Chebyshev spectral method for the controlled Duffing oscillator ⋮ A numerical solution of the nonlinear controlled Duffing oscillator by radial basis functions ⋮ A Chebyshev spectral method for the solution of nonlinear optimal control problems ⋮ Periodic doubling solutions in the Duffing oscillator: A Galerkin approach ⋮ The Lie-group shooting method for solving multi-dimensional nonlinear boundary value problems ⋮ Numerical solution of the controlled Duffing oscillator by hybrid functions ⋮ A Chebyshev technique for the solution of optimal control problems with nonlinear programming methods ⋮ Numerical Solution of the Controlled Rayleigh Nonlinear Oscillator by the Direct Spectral Method ⋮ Numerical Solution of the Controlled Rayleigh Nonlinear Oscillator by the Direct Spectral Method ⋮ A new sliding control strategy for nonlinear system solved by the Lie-group differential algebraic equation method ⋮ Radial basis functions approach on optimal control problems: a numerical investigation ⋮ Estimation of the mechanical parameters of the human respiratory system ⋮ A Chebyshev expansion method for solving nonlinear optimal control problems.

Cites Work

• Stabilization of Cowell's classical finite difference method for numerical integration
• Differential tones in a damped mechanical system with quadratic and cubic non-linearities
• Numerical computation of forced oscillations in coupled Duffing equations
• Two mode subharmonic vibrations of order a non-linear beam forced by a two mode harmonic load
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