Novel Chebyshev wavelets algorithms for optimal control and analysis of general linear delay models

Abstract

A new efficient type of Chebyshev wavelet is used to find the optimal solutions of general linear, continuous-time, multi-delay systems with quadratic performance indices and also to obtain the responses of linear time-delay systems. According to the new definition of Chebyshev wavelets, the operational matrices of integration, product, delay and inverse time and the integration matrix are derived. Furthermore, new operational matrices as the piecewise delay operational matrix and the stretch operational matrix of the desired Chebyshev wavelets are introduced to analyze systems with, in turn, piecewise constant delays and stretched arguments or proportional delays. Two novel algorithms based on newly Chebyshev wavelet method are proposed for the optimal control and the analysis of delay models. Some examples are solved to establish that the accuracy and applicability of Chebyshev wavelet method in delay systems are increased.