Chebyshev polynomials and spectral method for optimal control problem

Abstract EN

Abstract This paper presents efficient algorithms which are based on applying the idea of spectral method using the Chebyshev polynomials: including Chebyshev polynomials of the first kind, Chebyshev polynomials of the second kind and shifted Chebyshev polynomials of the first kind.

New properties of Chebyshev polynomials are derived to facilitate the computations throughout this work.

In addition the convergence criteria for the proposed algorithms are derived.

The use of the three algorithms has been demonstrated with example. Keywords: spectral method chebyshev polynomials quadratic optimal control