Chebyshev pseudospectral method
The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials. Unlike the Legendre pseudospectral method, the Chebyshev pseudospectral (PS) method does not immediately offer high-accuracy quadrature solutions. Consequently, two different versions of the method have been proposed: one by Elnagar et al,[1] and another by Fahroo and Ross.[2]. The two versions differ in their qudrature techniques. The Fahroo-Ross method is more commonly used today due to the ease in implementation of the Clenshaw-Curtis quadrature technique (in contrast to Elnagar's cell-averaging method).
References
- ^ G. Elnagar and M. A. Kazemi, Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems, Computa- tional Optimization and Applications, Vol. 11, 1998, pp. 195-217.
- ^ F. Fahroo and I. M. Ross, Direct trajectory optimization by a Chebyshev pseudospectral method, Journal of Guidance, Control, and Dynamics, Vol. 25, No. 1, pp. 160-166, 2002.