Application of discrete Chebyshev polynomials to the optimal control of digital systems

Abstract

The shift transformation matrix for discrete Chebyshev polynomials is introduced in this study. The discrete variational principle combined with the idea of penalty function is taken to construct the modified discrete Euler-Lagrange equations. Then, the discrete Chebyshev series are applied to simplify the modified equations into a set of linear algebraic ones for the approximations of state and control variables of digital systems. It is seen that this technique is quite straightforward and simple, and computing time can be saved considerably.