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Optimal input signal design for fractional-order system identification

Jakowluk W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 1

37--44

The optimal design of excitation signal is a procedure of generating an informative input signal to extract the model parameters with maximum pertinence during the identification process. The fractional calculus provides many new possibilities for system modeling based on the definition of a derivative of noninteger-order. A novel optimal input design methodology for fractional-order systems identification is presented in the paper. The Oustaloup recursive approximation (ORA) method is used to obtain the fractional-order differentiation in an integer order state-space representation. Then, the presented methodology is utilized to solve optimal input design problem for fractional-order system identification. The fundamental objective of this approach is to design an input signal that yields maximum information on the value of the fractional-order model parameters to be estimated. The method described in this paper was verified using a numerical example, and the computational results were discussed.

Strict Maximum Separability of Two Finite Sets: An Algorithmic Approach

Cendrowska D.

International Journal of Applied Mathematics and Computer Science

2005

Vol. 15, no 2

295-304

The paper presents a recursive algorithm for the investigation of a strict, linear separation in the Euclidean space. In the case when sets are linearly separable, it allows us to determine the coefficients of the hyperplanes. An example of using this algorithm as well as its drawbacks are shown. Then the algorithm of determining an optimal separation (in the sense of maximizing the distance between the two sets) is presented.