In this paper, a novel direct scheme to solve a set of time-delay fractional optimal control problems is introduced. The method firstly uses a set of Dickson polynomials as basis functions to approximate the states and control variables of the system. Next, the context of these basis functions and the use of a collocation method allow to transform the problem into a system of nonlinear algebraic equations. Finally, the unknown coefficients and control parameters in the original problem can be easily estimated by resolving the new system of equations. Given the high efficiency of the Dickson polynomials to deal with time-delay fractional systems, the proposed strategy involves a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The convergence analysis of the proposed method is presented, along with some illustrative examples which demonstrate its most relevant features.
Nowadays, advances in different fields of technology have increased demands for reliable controllers. Uncertainty and disturbances, which are inevitable in most real‐world systems, as well as increasing complexity in the dynamics of many systems, are requiring the design and application of intelligent controllers. Fuzzy controllers, and specifically type‐2 fuzzy control techniques, could play a beneficial role in a variety of control purposes, since they are robust against uncertainties. Therefore, an immense body of research is devoted to these fuzzy control techniques. This paper introduces a comprehensive review about the most recent advances in the design and implementation of type‐2 fuzzy control schemes both for integer‐ and fractional‐order systems. Thus, in addition to the past and present achievements in this context, future trends are also delineated. Moreover, most important works dealing with type‐2 fuzzy controller are discussed, and their advantages and drawbacks are outlined. Consequently, we firmly believe the present paper will pave the way for future research in this area.
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