International Journal of Control special issue on "Applied Fractional calculus in Modelling, Analysis and Design of Control Systems" published
vol. 90, issue 6.
Fractional calculus is about differentiation and integration of non-integer orders. Using integer-order models and controllers for complex natural or man-made systems is simply for our own convenience. Using integer-order traditional tools for modelling and control of dynamic systems may result in suboptimum performance, that is, using fractional-order calculus tools, we can be ‘more optimal’ as already documented in the literature. An interesting remark is that, using integer-order traditional tools, more and more ‘anomalous’ phenomena are being reported or complained but in applied fractional calculus community, it is now more widely accepted that ‘anomalous is normal’ in nature. We believe, beneficial uses of this versatile mathematical tool of fractional calculus from an engineering point of view are possible and important, and fractional calculus may become an enabler for new science discoveries.
As applications of fractional calculus in various subjects increase, it is now no longer possible to turn a blind eye to the dynamical perfusion of fractional calculus from the ‘soft’ application fields of medicine, chemistry, biology, into ‘hard’ application field of production machines and industrial systems to the process industry. Within this fiddler's paradise of challenges and opportunities, the emerging tools from fractional calculus seem to be becoming ubiquitous in the playground of the modern control engineers.
This special issue, with its revealing content and up-to-date developments, joins the utmost proof for this distinctive tendency of adoption of fractional calculus. Since 2012, several such special issues were published in some leading journals which showcase the active interference of fractional calculus to control engineering. The special issue organized in IJC answers the need for latest developments in control area. This focused special issue on control theory and applications is yet another effort to bring forward the latest updates of the applied fractional calculus community. For that we feel very excited and we hope the readers will feel the same.
Independent of the application field, control is a hidden technology, which runs through and connects them all together in a tremendously successful field of applications. By adding this emerging tool of fractional calculus, the readers may find themselves in front of a catalytic reaction of new developments waiting to be explored.
The special issue call received 32 submissions of which 10 were accepted. This high rejection ratio (69%) indicates a high quality of the selected papers. These can be classified into (1) mathematical and numerical formulations and (2) applications.
From the first group, the paper of Chen et al. presents a review of the numerical tools for evaluating fractional-order systems and controllers. It provides the reader with an up-to-date database of information as to where and what can be used for specific purposes. Useful numerical formulations to simulate complex differential equations of fractional-order are given in Dingyu and Lu. Answering a similar problem, Baleanu et al. present novel solution to fractional optimal control problems by means of the Chebyshev–Legendre technique. In the same line of computational thought, the work of Visioli et al. provides a generalised isodamping tuning rule for the fractional-order controllers.
From the second group, there are six applications discussed in this special issue. A fractional-order swarm system with uniform time delays is analyzed in terms of stability in Tavazoei and Naderi. The famous N-link pendulum with its strong nonlinear dynamics is presented in the form of a fractional-order system in Machado and Lopes and control of a robotic antenna is presented in Feliu-Batlle and Feliu-Talegon. In Ge et al., for a class of fractional sub-diffusion equations, how actuator configuration affects approximate controllability property is discussed. Lu and Zhao presented a decentralized robust H-infinity control method for fractional-order interconnected systems with uncertainties. Finally, Chen, Wu and et al. studied a pinning synchronization method for fractional-order delayed complex networks with non-delayed and delayed couplings.
The aim of this special issue is to show the control engineering research community the usefulness of these fractional-order tools in a pragmatic context, in order to stimulate further adoptions and applications. It is our sincere hope that this special issue will become a milestone of a significant trend in the future development of classical and modern control theory. The special issue points out the trend of the fractional-order control community to extend and generalise classical and modern control theory to fractional order systems. The selected contributions may stimulate future industrial applications of the fractional order control leading to simpler, more economical, reliable and versatile systems.
There is no doubt that with this special issue, the emerging concepts of fractional calculus will have their mathematical abstractness removed and become an attractive tool in the field of control engineering with more ‘good consequences.’
Other special issues published:
- 2016. IJC http://mechatronics.ucmerced.edu/news/2017/international-journal-control-special-issue-guest-coedited-dr-chen-published
- 2013. Mechatronics,Volume 23, Issue 7, Pages 739-916 (October 2013). Fractional Order Modeling and Control in Mechatronics
- 2013. Li, Changpin; Chen, YangQuan; Kurths, Juergen. Fractional calculus and its applications. Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences Volume: 371 Issue: 1990 Published: MAY 13 2013. DOI: 10.1098/rsta.2013.0037
- 2012. Changpin Li*, YangQuan Chen, Igor Polubny and Blas Vinagre. “Introduction to Special Issue: Fractional Dynamics and Control” International Journal of Bifurcation Chaos, Special Issue on “Fractional Dynamics and Control”, April issue of 2012. (4 pages) DOI: 10.1142/S0218127412020026
- 2011. Editorial. Guest – Editors: Virginia Kiryakova, Yury Luchko, Francesco Mainardi, Blas Vinagre, Igor Podlubny, YangQuan Chen. SPECIAL ISSUE Dedicated to 80th Anniversary of Professor Rudolf Gorenflo. Fractional Calculus and Applied Analysis. Volume 14 / 2011 DOI: 10.2478/s13540-011-0001-0.