Analysis and optimal control of discrete linear time-varying systems via discrete general orthogonal polynomials

Abstract

General discrete orthogonal polynomials are introduced to analyse and to approximate the solution of a class of linear time-varying discrete systems. It is shown that the proposed method is very general in that it works for any discrete orthogonal polynomial that possess a recurrence relation. Hence the present method includes the results obtained by use of discrete Chebyshev polynomials and discrete Laguerre polynomials as special cases. The analysis of linear time-varying systems via general discrete orthogonal polynomials is presented. General discrete orthogonal polynomials are then applied to approximate the solution of time-varying optimal-control problems. Illustrative examples are included and a comparison of the results obtained via several different orthogonal polynomials is presented.