Shifted modified chebyshev direct method for solving quadratic optimal control problem

Abstract

The area of Chebyshev polynomial functions plays an important role in mathematic with applications in computer science and engineering. New shifted modified Chebyshev polynomials are considered in the present article. An explicit expression of the definition for shifted modified Chebyshev polynomials with some important relations and interesting properties is first derived. Then new expression formulation for constructing shifted modified Chebyshev operation matrix of derivative is given. Such polynomials are used as basis functions to propose and analyze direct numerical technique to optimal control problem having a quadratic performance index, based on shifted modified Chebyshev polynomials together with its operation matrix of derivative, such a problem is reduced into an optimization  technique which can be solved easily using quadratic programming  algorithm. For confirming the validity and accuracy of the presented method some numerical examples are included a long with a comparison between the obtained results against the exact one.