×

On overparametrization of nonlinear discrete systems. (English) Zbl 0933.37055

Summary: One of the subjects which has received a great deal of attention is the overparametrization problem. It is known that the dynamical performance of the model representations deteriorates if the respective model structure is too complex. This paper investigates the problem of model overparametrization. Two new types of overparametrization, fixed-point and dimension overparametrization, are introduced and based upon this a new procedure for improving structure detection of nonlinear models is developed. This procedure uses all the information from the cluster cancellation and the location of the fixed points. Numerous examples are given to illustrate the ideas.

MSC:

37G35 Dynamical aspects of attractors and their bifurcations
37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
37N35 Dynamical systems in control
93C35 Multivariable systems, multidimensional control systems
93E12 Identification in stochastic control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1103/PhysRevE.47.3057
[2] DOI: 10.1142/S0218127493000428 · Zbl 0900.58021
[3] DOI: 10.1142/S0218127494000617 · Zbl 0900.70335
[4] DOI: 10.1080/00207179508921557 · Zbl 0837.93009
[5] DOI: 10.1142/S0218127496000059 · Zbl 0870.58091
[6] DOI: 10.1080/00207728808964057 · Zbl 0669.93015
[7] DOI: 10.1016/0888-3270(89)90012-5
[8] DOI: 10.1016/0375-9601(90)90841-B
[9] DOI: 10.1103/PhysRevA.43.2787
[10] DOI: 10.1103/PhysRevLett.65.1523 · Zbl 1050.37520
[11] DOI: 10.1142/S021812749300043X · Zbl 0900.70332
[12] DOI: 10.1080/00207178908559683 · Zbl 0674.93009
[13] Chua L. O., IEEE Trans. Circuits Syst. 40(10-11). (1993)
[14] DOI: 10.1103/RevModPhys.57.617 · Zbl 0989.37516
[15] DOI: 10.1103/PhysRevA.34.4971
[16] Gencay R., Physica 59 pp 142– (1992)
[17] DOI: 10.1142/S0218126693000150
[18] DOI: 10.1007/BF01608556 · Zbl 0576.58018
[19] DOI: 10.1098/rsta.1979.0068 · Zbl 0423.34049
[20] DOI: 10.1142/S0218127493000507 · Zbl 0875.58025
[21] Kantz H., Phys. Rev. 185 pp 77– (1994)
[22] DOI: 10.1142/S0218127493000507 · Zbl 0875.58025
[23] Kennel M. B., Technical Report, Institute of Nonlinear Science, University of California, San Diego, La Jolla, CA pp 92093– (1994)
[24] Kennel M. B., Technical Report, Institute of Nonlinear Science, University of California, San Diego, La Jolla, CA pp 92093– (1992)
[25] Kruel T. M., Physica 63 pp 117– (1993)
[26] DOI: 10.1080/0020718508961129 · Zbl 0569.93011
[27] Lorenz E. N., J. Atmos. Sci. 20 pp 131– (1963)
[28] DOI: 10.1142/S021812749300057X · Zbl 0875.62426
[29] DOI: 10.1142/S021812749300057X · Zbl 0875.62426
[30] DOI: 10.1142/S0218127497001758 · Zbl 0976.93501
[31] DOI: 10.1142/S0218127492000148 · Zbl 0878.34047
[32] DOI: 10.1142/S0218126693000319
[33] DOI: 10.1103/PhysRevLett.55.1082
[34] DOI: 10.1143/PTP.77.1
[35] Tong H., Physica 58 pp 299– (1992)
[36] DOI: 10.1016/0020-7462(85)90024-1
[37] Wolf A., Physica 16 pp 285– (1985)
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.