Prof. Mohsen Razzaghi,
Head of Department of Mathematics and Statistics,
Mississippi State University MS 39762, USA,
Currently, Fulbright Scholar,
Department of Mathematics and Computer Science, Technical
University of Civil Engineering, Bucharest, Romania
Titlul: "Hybrid functions and wavelets in control problems"
Rezumat:
Orthogonal functions have been applied to solve various problems of the dynamical systems. Much attention has been given to the solution of control problems. The approach is to convert the control problems to an algebraic equation. Signals frequently have mixed features of continuity and jumps. In such situations neither the continuous basis functions(such as Chebyshev, Laguerre, Legendre, etc) nor piecewise basis functions (such as block-pulse, Haar, Walsh, etc) taken alone would form an efficient basis in the representation of such signals. Recently, different types of hybrid functions (which are the combinations of block-pulse functions and continuous basis functions) and different types of wavelets (with continuous basis functions as mother wavelets) have been used for solving control problems and proved to be a mathematical power tool.
In this talk we present the Legendre wavelets and hybrid functions of block-pulse with Legendre polynomials and block-pulse with Bernoulli polynomials. Numerical examples are included to demonstrate the applicability and the accuracy of the proposed method and a comparison is made with the existing results.
