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 |