Optimal Controllers with Complex Order Derivatives

Abstract

This paper studies the optimization of complex-order algorithms for the discrete-time control of linear and nonlinear systems. The fundamentals of fractional systems and genetic algorithms are introduced. Based on these concepts, complexorder control schemes and their implementation are evaluated in the perspective of evolutionary optimization. The results demonstrate not only that complex-order derivatives constitute a valuable alternative for deriving control algorithms, but also the feasibility of the adopted optimization strategy.

Fractional generalization of memristor and higher order elements

“…Nevertheless, there is already the proposal for including complex order operators in control algorithms [89]. On the other hand, the influence of the memory build in the nonlinear dynamics and the memory intrinsic to FC may also to be further explored.…”

Complex order fractional derivatives in viscoelasticity

“…However, most of the work done in this field so far has been based on the use of real order fractional derivatives and integrals. It is worth to mention that there are several authors who also applied complex order fractional derivatives to model various phenomena, see the work of Machado or Makris, [20,23,24]. In all of these papers, restrictions on constitutive parameters that follow from the Second Law of Thermodynamics were not examined.…”

Convergence analysis and approximation solution for the coupled fractional convection-diffusion equations

“…Recently, fractional calculus is a powerful tool to investigate the dynamics of complex systems in different sciences such as fluid mechanics, economic and biology ( for example, see [4,11,13,14,15,19,21,22] and therein references). Many of biology researchers have used to model real process by fractional calculus.…”