A cell-averaging Chebyshev spectral method for the controlled Duffing oscillator
In recent times there is much interest in the use of spectral methods for the solution of nonlinear physical and engineering problems. This trend is more evident in the area of optimization in which highly accurate solutions are needed. However, serious analytical and numerical difficulties, such as accumulation of roundoff or truncation errors, need to be overcome before optimal control approaches will find widespread practical implementation, especially for nonlinear optimal control problems such as the controlled Duffing oscillator problem. The controlled Duffing oscillator, is known to describe many important oscillating phenomena in nonlinear engineering systems. This paper presents a spectral method of solving the controlled Duffing oscillator. The method is based upon constructing the \(M\)-th 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 other numerical schemes.
cell-averaging Chebyshev spectral method
scientific article; zbMATH DE number 826018
scientific article