A method for sub-optimal control of the delayed fractional order linear time varying systems with computation reduction approach

A method for designing suboptimal control for a class of delayed fractional systems is proposed in this paper. Despite theoretical advances in fractional mathematics and computational techniques for solving fractional optimal control (FOC) problems, as well as a lack of comprehensive analytical methods, numerical methods have been developed. For this purpose, in this study, the necessary optimal conditions for the time-delay fractional optimal control (TDFOC) problem are presented first; Then an algorithm for the numerical solution to this problem is suggested. This algorithm is based on a fractional derivative approximation and linear interpolation for delayed arguments. According to this method, the TDFOC problem is transformed into a system of algebraic equations that can be solved numerically. The proposed method's efficiency is assessed by solving several numerical examples.