Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems

Abstract

• A new set of basis functions called the piecewise Chebyshev cardinal functions is introduced. • These basis functions possess many useful properties, such as orthogonality, cardinality and spectral accuracy. • The operational matrix of fractional integration is obtained for these functions. • A direct matrix method is developed to investigate a class of constrained fractional optimal control problems. In this paper, a new set of basis functions called the piecewise Chebyshev cardinal functions is generated to investigate a class of constrained fractional optimal control problems. These basis functions possess many useful properties, such as orthogonality, cardinality and spectral accuracy. The fractional integral matrix of these functions is obtained. A direct scheme based on the these basis functions together with their fractional integral matrix is developed for solving the problem under consideration. The established method transforms solving the original problem into solving a constrained minimization problem by approximating the state and control variables in terms of the piecewise Chebyshev cardinal functions. Some numerical examples are given to show the efficiency of the proposed technique.