Working Groups 1

WG1 – Fractional calculus and mathematical models

WG1 will improve existing and develop new methods for solving non-integer differential equations. WG1 will also provide an application oriented view on the theory of fractional equations to model the behaviour of various function circuits, control, and to describe the processes investigated within other working groups. The activities of WG1 are divided into the following tasks:
-Task 1.1 Mathematical methods of fractional order integration and differentiation
-Task 1.2 Fractional order controllers
-Task 1.3 Parameter estimation and modeling of real processes and systems
-Task 1.4. Developing efficient and accurate numerical schemes
-Task 1.5 Development of toolboxes for MATLAB
-Task 1.6 Fractionalizing standard models
-Task 1.7 Investigation of preservation of properties of non-integer order control and dynamical systems, characterizations and algorithms under discretization

 

The deliverables of WG1 can be summarized as follows:

No. Title Description M.
D1.1 Off-line identification Development and implementation of a general framework for  global, non-adaptive identification of fractional and non-rational systems in general 10
D1.2 Y1 WS proceedings Contribution by WG1 to the proceedings of Year 1 WS 12
D1.3 Adaptive identification Development and implementation of a general framework of  adaptive identification of fractional and non-rational systems 20
D1.4 Y2 WS proceedings Contribution by WG1 to the proceedings of Year 2 WS 24
D1.5 FO methods and

models

Approximation of derivatives and integrals of fractional orders by new numerical and analytical methods; Fractionized models 36
D1.6 Y3 WS proceedings Contribution by WG1 to the proceedings of Year 3 WS 36
D1.7 Discrete FOs Development of methods for PID controllers’ synthesis, Matlab toolboxes, discretization algorithms 46
D1.8 Y4 WS proceedings Contribution by WG1 to the proceedings of Year 4 WS 48
D1.9 Action book input Contribution by WG1 to the final Action book 48