Objectives – progress

Organizing join events within the COST Action CA15225 and using its networking tools to foster interaction between the COST Action members being interested in fractional calculus, fractional systems’ and models’ design,  and their utilization, the individual tasks of each Working Group are being solved to gain the expected deliverables and achieve the Research coordination and/or Capacity building objectives as listed below:

Research coordination objectives:

O1 – Define optimization steps leading to efficient implementation of fractional-order systems

Being active in the analysis of approximation techniques of fractional-order function blocks, the design process is being defined that results in description and realization of fractional-order systems that may be understood as optimal from the viewpoint of the final complexity as depending on the expected the utilization, the system features the minimal order of approximation by maintaining the maximal allowed error in approximation in the required frequency band compared to ideal behavior. Further achievements are expected through efficient cooperation in the Action network by providing deap analysis of other approximation methods and defining the routines leading to optimal fractional-order systems design.

The current level of achievement of this Objective is undestood to be 26-50%

O2 – Improve characteristics of fractional-order controllers that can be employed in different industrial loops or in electro-mechanical systems

Through the progress reached mainly by the deliverables D4, D7, D8, D12 and D17 the tools and design steps were described that enable efficient design of fractional-order controllers featuring required properties.

The current level of achievement of this Objective is undestood to be 51-76%.

O3 – Develop tools to define dynamic simulation models, control schemes and algorithms

A first set of Matlab tools for the simulation of fractional-order systems has been released and is now available. Since Matlab does not provide built-in routines for fractional-order problems, these tools developed thanks to the Cost Action enable the scientific community and the industry to efficiently solve problems for which in the past every user had to write their own code with great difficulties. The tools are published on-line here.

The current level of achievement of this Objective is undestood to be 26-50%.

O4 – Design and implement fractional-order controllers for industrial processes

Using the design processes to propose fractional-order controllers with improved characteristics, the implementation of fractional-order PID controllers was shown. As examples, a re-configurable fractional-order PI controller, suitable for brake and throttle control in an autonomous vehicle was discussed in 10.1019/ECCTD.2017.8093229. Other successful implementation of fractional controllers can be found in 10.1016/j.aeue.2017.03.010, 10.1109/TSP.2017.8076078, or 10.1016/j.ifacol.2017.08.2084.

The current level of achievement of this Objective is undestood to be 51-76%.

O5 – Design and characterize new fractional-order elements using prospective technologies in order to obtain robust and commercial devices

The hardware design of fractional-order elements based on the Resistive-Capacitive Elements with Distributed Parameters (RC-EDP) was investigated, whereas a software enabling to define the geometry, interconnection of sections and the resistive/capacitive layers’ parameters was developed in cooperation between the Czech and Russian research groups. Currently, within a national project (funded by the Czech Science Foundation) the selected structures are being designed and produced as laboratory samples to prove the proper behavior and operability of the software design tool.

The current level of achievement of this Objective is undestood to be 26-50%.

O6 – Utilize fractional-order adjustment rule to model reference adaptive control in engineering applications

Studies investigated the utilization of fractional-order modeling in conventional MRAC structure and demonstrated contributions of incorporation of FOPID control and fractional-order MRAC structure to fault-tolerance and disturbance rejection control performance. We observed that when the reference model of MRAC is chosen as a fractional-order model, the multi-loop MRAC-FOPID control structures can improve robust performance of FOPID control system. For example, the following outputs can be gived as results of join research oriented activities: 10.1109/TSP.2017.8076078, 10.1109/TSP.2017.8076080.

The current level of achievement of this Objective is undestood to be 51-75%.

O7 – Implement fractional-order digital/analogue function blocks especially in medical signal processing

This objective is being achieved through the definition and utilization of fractional-order models and emulators. Significant contribution to this topic was done by the Greek and Egypt group presented in “Design of CMOS Analog Integrated Fractional-Order CircuitsApplications in Medicine and Biology” (10.1007/978-3-319-55633-8). This objectives is also being achieved in cooperation with our USA International Partner. Studies applying optimization routines to electrical impedance data collected from human tissues before and after fatiguing exercises have been explored. The application of the optimization routines have shown that fractional-order models provide an excellent fit to these collected datasets from both pre-fatigue and post-fatigue states. These tools and processing methods have the potential to support wider applications for medical monitoring related to quantifying tissue changes, whereas the initial results of these studies can be found here: 10.3390/fractalfract2040027 and 10.1088/2057-1976/aa971b.

The current level of achievement of this Objective is undestood to be 26-50%.

O8 – Utilize fractional-order models and systems in bioengineering and biomedical applications

A framework for modelling velocity profiles of suspended objects in Non-Newtonian fluid environment for impedance measurement and subsequently determining changes in concentration profiles as a function of time and space. In collaboration with Technical University of Cluj Napoca a lab scale prototype of a robot swimming in non-newtonian fluids has been developed. The fractional derivative model for velocity and friction drag effect upon a suspended object are derived.

A mathematical model of nociception pathway and a prototype device for pain measurement have been developed. The method and model indicate that nociceptor stimulation perceived as pain in awake healthy volunteers is non-invasively detected. Further, clinical trial are being prepared to validate the model and device in clinical settings.

Tools emerging from fractional calculus have been employed to model changes in chronic obstructive pulmonary disease (COPD) and to understand their effect on model parameters values. The theoretical basis helps in understanding the interplay between all these structural and dynamical changes.

Parkinsonic dysgraphia affects the majority of Parkinson’s disease (PD) patients as a result of handwriting abnormalities mainly caused by motor dysfunctions. Several effective approaches of quantitative PD dysgraphia analysis, such as online handwriting processing, have been utilized. In our research, we aim to deeply explore the impact of advanced online handwriting parametrization based on fractional order derivatives (FD) on the PD dysgraphia diagnosis and its monitoring, whereas the initial results are to be presented in “Identification and Monitoring of Parkinson’s Disease Dysgraphia Based on Fractional Order Derivatives of Online Handwriting”, Applied Science Journal.

In paper “A new fractional model and optimal control of a tumor–immune surveillance with non–singular derivative operator” by D. Baleanu, A. Jajarmi, S.S.  Sajjadi and D. Mozyrska, submitted to the journal: “Chaos: An Interdisciplinary Journal of Nonlinear Science” we present a new fractional–order mathematical model for a tumor–immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and non–singular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag–Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurate than the other fractional– and integer–order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined.

The current level of achievement of this Objective is undestood to be 51-75%.

O9 – Characterize preservation properties of non-integer order control and dynamical systems under discretization

The first achievements are reached by the cooperation between the Romanian and Polish groups. The results discussed in the paper “Stability and numerical solutions to the variable-order Caputo fractional difference equations with order values from (1, 2]” by Oana Brandibur, Eva Kaslik, Dorota Mozyrska and Małgorzata Wyrwas from West University of Timisoara, Romania and Bialystok University of Technology, Poland, accepted to NODYCON2019 Proceedings to be published in the SpringerLink digital library and as hard copies will be indexed in Scopus, Web of Science, Google Scholar, present and characterize the problem of stability of the Caputo type linear variable-, fractional-order discrete-time equations. An analysis for orders from the interval (1, 2] is considered. For the stability analysis of the considered equations the Z -transform is used. The sufficient conditions for the asymptotic stability are presented.

The current level of achievement of this Objective is undestood to be 26-50%.

Capacity building objectives:

O10 – Establishment of European-wide scientific and technology knowledge platform in order to instigate interdisciplinary interaction for the development of innovative fractional-order systems

Within the two-year period the COST Action managed to address a significant number of researchers from mathematicians to applied research engineers spanning from different R&D areas. Through the interaction of these researches at the events organized within the Action and mainly the STSM networking tool, new international and interdisciplinary research groups stated to be created that result in join publications and project proposals, some of them successfully funded.

The current level of achievement of this Objective is undestood to be 51-75%.

O11 – Bridging separate research fields and disciplines to present interdisciplinary approach to scientific research and foster multidisciplinary breakthroughs

The participants using their current knowledge within their research areas were capable to continue in fulfilling the tasks of individual Work Groups with low interaction with other colleagues being active in other Work Groups, so far. However, already first successful cooperation can be identified in hardware design of PID controllers being presented in join publications. The future join research resulting in new multidisciplinary breakthroughs that are expected to be reached within the join research projects that started to be solved during the year 2018 first.

The current level of achievement of this Objective is undestood to be 26-50%.

O12 – Ensure Early Career Investigators to participate in the Action within dedicated dissemination and formation activities such as workshops or STSMs and give them the best possible return in terms of scientific knowledge, research direction and coordination skills

At the regularly events organized by the Action the ECIs and/or already current PhD students are supported to participate and share their knowledge with other young colleagues but also gain experience from the senior researchers. The STSM shows to be a very beneficial tool for individuals that visit a partner institutions and deal join research activities. The use of ICT Conference Grants also proves to be useful primarily for active researchers and their presentation of results at international conferences but secondly also to disseminate the ideas of the network being under umbrella of this Action with the offer of accepting new members/persons taking the advantage of their participation at the future events organized by the Action.

The current level of achievement of this Objective is undestood to be 51-75%.

O13 – Increase the gender balance in terms of researchers involved in Action activities, both in terms of technical and scientific contribution as well as of research direction and Action governance

By the time of the last MC meeting organized in Bialystok, Poland (Sept. 19, 2018), the current gender balance with the ratio M:F was identified to be 74:26 and gets closer to the ratio being understood as optimal, i.e. 60:40 to 40:60, as in the previous monitoring period the M:F ratio was 77:23. Organizing the future events should further improve the gender balance as at the previous MC meetings it was pointed that the gender balance cannot be evaluated only among the MC Members and MC Substitutes of the Action but also all other participants at the events organized by the Action and using the networking tools must be counted.

The current level of achievement of this Objective is undestood to be 51-75%.