Petrov, Valery; Showalter, Kenneth Nonlinear prediction, filtering, and control of chemical systems from time series. (English) Zbl 0938.37055 Chaos 7, No. 4, 614-620 (1997). Summary: Prediction, filtering and control of nonlinear systems is formulated in terms of corresponding nonlinear surfaces in the phase space of delayed system readings and control parameters. The construction of these surfaces from time series and their use is demonstrated with a simple chemical model in the chaotic regime. Cited in 1 Document MSC: 37M10 Time series analysis of dynamical systems 37N35 Dynamical systems in control Keywords:control parameters; time series; chemical chaos; chaotic regime; nonlinear control; nonlinear prediction; nonlinear filtering PDFBibTeX XMLCite \textit{V. Petrov} and \textit{K. Showalter}, Chaos 7, No. 4, 614--620 (1997; Zbl 0938.37055) Full Text: DOI Link References: [1] Abarbanel H. D. I., Rev. Mod. Phys. 65 pp 1331– (1993) · doi:10.1103/RevModPhys.65.1331 [2] DOI: 10.1103/PhysRevLett.64.1196 · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196 [3] DOI: 10.1063/1.881461 · doi:10.1063/1.881461 [4] DOI: 10.1063/1.881461 · doi:10.1063/1.881461 [5] DOI: 10.1063/1.881461 · doi:10.1063/1.881461 [6] So P., Phys. Rev. E 51 pp 2955– (1995) · doi:10.1103/PhysRevE.51.2955 [7] Petrov V., Phys. Rev. E 51 pp 3988– (1995) · doi:10.1103/PhysRevE.51.3988 [8] Petrov V., Phys. Rev. Lett. 75 pp 2895– (1995) · doi:10.1103/PhysRevLett.75.2895 [9] Ding M., Phys. Rev. E 53 pp 4334– (1996) · doi:10.1103/PhysRevE.53.4334 [10] DOI: 10.1103/PhysRevLett.45.712 · doi:10.1103/PhysRevLett.45.712 [11] Peng B., J. Phys. Chem. 94 pp 5243– (1990) · doi:10.1021/j100376a014 [12] Gray P., Chem. Eng. Sci. 39 pp 1087– (1984) · doi:10.1016/0009-2509(84)87017-7 [13] Petrov V., J. Chem. Phys. 97 pp 6191– (1992) · doi:10.1063/1.463727 [14] DOI: 10.1103/PhysRevA.46.3057 · doi:10.1103/PhysRevA.46.3057 [15] DOI: 10.1016/0167-2789(83)90125-2 · doi:10.1016/0167-2789(83)90125-2 [16] Petrov V., Phys. Rev. Lett. 76 pp 3312– (1996) · doi:10.1103/PhysRevLett.76.3312 [17] Petrov V., Phys. Rev. Lett. 77 pp 3779– (1996) · doi:10.1103/PhysRevLett.77.3779 [18] Schreiber T., Phys. Rev. E 53 pp R4326– (1996) · doi:10.1103/PhysRevE.53.R4326 [19] Hunt K. L. C., J. Chem. Phys. 96 pp 7019– (1992) · doi:10.1063/1.462535 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.