Karimi, H. R.; Lohmann, B.; Moshiri, B.; Maralani, P. Jabehdar Wavelet-based identification and control design for a class of nonlinear systems. (English) Zbl 1137.93318 Int. J. Wavelets Multiresolut. Inf. Process. 4, No. 1, 213-226 (2006). Summary: We extend the wavelet networks for identification and \(H_{\infty}\) control of a class of nonlinear dynamical systems. The technique of feedback linearization, supervisory control and \(H_{\infty}\) control are used to design an adaptive control law and also the parameter adaptation laws of the wavelet network are developed using a Lyapunov-based design. By some theorems, it will be proved that even in the presence of modeling errors, named network error, the stability of the overall closed-loop system and convergence of the network parameters and the boundedness of the state errors are guaranteed. The applicability of the proposed method is illustrated on a nonlinear plant by computer simulation. Cited in 6 Documents MSC: 93B30 System identification 93B36 \(H^\infty\)-control 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:system identification; supervisory control; \(H_{\infty}\) control; stability analysis; wavelet network PDFBibTeX XMLCite \textit{H. R. Karimi} et al., Int. J. Wavelets Multiresolut. Inf. Process. 4, No. 1, 213--226 (2006; Zbl 1137.93318) Full Text: DOI References: [1] DOI: 10.1109/TCS.1986.1086019 · Zbl 0613.65072 · doi:10.1109/TCS.1986.1086019 [2] DOI: 10.1080/00207160211932 · Zbl 0995.65145 · doi:10.1080/00207160211932 [3] DOI: 10.1007/s10883-005-4172-z · Zbl 1063.49002 · doi:10.1007/s10883-005-4172-z [4] DOI: 10.1080/00207160512331323407 · Zbl 1070.65052 · doi:10.1080/00207160512331323407 [5] DOI: 10.1080/03057920412331272225 · Zbl 1068.65088 · doi:10.1080/03057920412331272225 [6] DOI: 10.1109/29.1644 · Zbl 0709.94577 · doi:10.1109/29.1644 [7] DOI: 10.1109/72.182697 · doi:10.1109/72.182697 [8] DOI: 10.1109/72.165591 · doi:10.1109/72.165591 [9] DOI: 10.1109/72.822511 · doi:10.1109/72.822511 [10] Cheng Y. M., Proc. Natl. Counc. 22 pp 783– [11] Burrus C. S., Introduction to Wavelets and Wavelet Transforms (1998) [12] DOI: 10.1109/9.746278 · Zbl 1056.93519 · doi:10.1109/9.746278 [13] DOI: 10.1109/72.363469 · doi:10.1109/72.363469 [14] DOI: 10.1109/9.481517 · Zbl 0842.93033 · doi:10.1109/9.481517 [15] DOI: 10.1016/0167-6911(88)90034-5 · Zbl 0634.93066 · doi:10.1016/0167-6911(88)90034-5 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.