×

Nonlinear identification using prior knowledge of fixed points: a multiobjective approach. (English) Zbl 1056.37091

Summary: This paper is devoted to the problem of model building from data produced by a nonlinear dynamical system. Unlike most published works that address the problem from a black-box perspective, in the present paper a procedure is developed that permits the use of prior knowledge about the location of fixed-points in addition to the data thus resulting in a gray-box approach. Numerical results using Chua’s double-scroll attractor and the sine map are presented. As discussed, the suggested procedure is useful as a means to partially compensate for the loss of information due to noise and to improve dynamical performance in the presence of model structure mismatches. Preliminary results have indicated that the procedure outlined in this paper is a systematic way of searching for models in the vicinity of the black-box solution. This could have important consequences not only in model building but also in model validation.

MSC:

37M10 Time series analysis of dynamical systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
90C29 Multi-objective and goal programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1142/S0218127496000059 · Zbl 0870.58091
[2] DOI: 10.1142/S0218127497001138 · Zbl 0965.93036
[3] DOI: 10.1142/S0218127498001790 · Zbl 0985.37094
[4] DOI: 10.1109/81.855463
[5] DOI: 10.1142/S021812740200419X
[6] DOI: 10.1080/00207178908559767
[7] DOI: 10.1142/S0218127499000894 · Zbl 0955.93502
[8] Broomhead D. S., Compl. Syst. 2 pp 321–
[9] DOI: 10.1103/PhysRevE.50.4488
[10] DOI: 10.1016/0167-2789(91)90222-U · Zbl 0736.62075
[11] Chankong V., Multiobjective Decision Making: Theory and Methodology (1983) · Zbl 0622.90002
[12] Chua L. O., IEEE Trans. Circuits Syst.-I 40 pp 10–
[13] DOI: 10.1063/1.1285863 · Zbl 1014.76094
[14] DOI: 10.1016/0167-2789(92)90085-2 · Zbl 0761.62118
[15] DOI: 10.1103/PhysRevE.49.4955
[16] DOI: 10.1016/S0167-2789(96)00248-5 · Zbl 1009.37501
[17] DOI: 10.1016/0005-1098(95)00146-8 · Zbl 0851.93024
[18] DOI: 10.1016/0167-2789(96)00054-1 · Zbl 0914.62063
[19] DOI: 10.1142/S021812749800070X · Zbl 0941.37056
[20] DOI: 10.1080/0020718508961130 · Zbl 0569.93012
[21] DOI: 10.1088/0305-4470/31/39/008 · Zbl 0936.81014
[22] DOI: 10.1103/PhysRevLett.45.712
[23] DOI: 10.1016/0167-2789(94)90226-7
[24] DOI: 10.1007/BF01053745 · Zbl 0943.37506
[25] DOI: 10.1109/81.404066
[26] DOI: 10.1007/BFb0091924
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.