Commenced in January 2007
Paper Count: 30172
A Generalized Approach for State Analysis and Parameter Estimation of Bilinear Systems using Haar Connection Coefficients
Abstract:Three novel and significant contributions are made in this paper Firstly, non-recursive formulation of Haar connection coefficients, pioneered by the present authors is presented, which can be computed very efficiently and avoid stack and memory overflows. Secondly, the generalized approach for state analysis of singular bilinear time-invariant (TI) and time-varying (TV) systems is presented; vis-╦£a-vis diversified and complex works reported by different authors. Thirdly, a generalized approach for parameter estimation of bilinear TI and TV systems is also proposed. The unified framework of the proposed method is very significant in that the digital hardware once-designed can be used to perform the complex tasks of state analysis and parameter estimation of different types of bilinear systems single-handedly. The simplicity, effectiveness and generalized nature of the proposed method is established by applying it to different types of bilinear systems for the two tasks.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083915Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1227
 Bing Cheng, Ning-Show Hsu, "Analysis and Parameter Estimation of Bilinear Systems via Block Pulse Functions", International J. of control, vol. 36, no. 1, pp. 53-65, 1982.
 Y.G. Jan, K.M. Wong, "Bilinear System Identification by Block Pulse Functions", J. of Franklin Institute, vol. 312, no. 5, pp. 349-359, 1991.
 F. L. Lewis, V. G. Mertzios, G. Vachtsevanos, M. A. Christodoulou, "Analysis of Bilinear Systems usingWalsh Functions", IEEE Transactions on Automatic Control, vol. 35, no. 1, pp. 119-123, 1990.
 F.L. Lewis, B.G. Mertzios, W. Marszakk, "Analysis of Singular Bilinear Systems using Walsh Functions", in IEE Proceedings-D, vol. 138, no. 2, pp. 89-92, 1991.
 B. Sepehrian, M. Razzaghi, "State Analysis of Time-Varying Singular Bilinear Systems by Single-Term Walsh Series", International Journal of Computer Mathematics, vol. 80, no. 4, pp. 413-418, 2003.
 V. R. Karanam, P. A. Frick, R R. Mohler, "Bilinear System Identification by Walsh Functions", IEEE Transactions On Automatic Control, vol. AC- 23, no. 4, pp. 709-713, 1978.
 Wen-Liang Chen, Yen-Ping Shih, "Parameter Estimation of Bilinear Systems via Walsh Functions", J. of Franklin Institute, vol. 305, no. 5, pp. 249-257, 1978.
 P. N. Paraskevopoulos, A. S. Tsirikos, K. G. Arvanitis, "A New Orthogonal Series Approach to State Space Analysis of Bilinear Systems", IEEE Transactions On Automatic Control, vol. 39, no. 4, pp. 793-797, 1994.
 J. Rico, G. T. Heydt, "Parameter Estimation using an Orthogonal Series Expansion", J. Electric Machines and Power Systems, vol. 28, pp. 761- 777, 2000.
 Chun-Hui Hsiao, Wen-June Wang, "State Analysis and Parameter Estimation of Bilinear Systems Via Haar Wavelets", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 47, no. 2, pp. 246-250, 2000.
 Chun-Hui Hsiao, Wen-June Wang, "State Analysis of Time-Varying Singular Bilinear Systems via Haar Wavelets", Mathematics and Computers in Simulation (MATCOM), vol. 52, pp. 11-20, 2000.
 I. Daubechies, "The Wavelet Transform, Time-Frequency Localization and Signal Analysis", IEEE Trans. Infor. Theory, vol. 36, pp. 961-1005, 1990.
 V. Murugesh, K. Batri, "State Analysis of Time-Varying Singular Bilinear Systems by RK-Butcher Algorithms", International Journal of Computers, Communications & Control, vol. III, no. 1, pp. 103-109, 2008.
 Jer-Nan Juang, "Continuous-Time Bilinear System Identification", Nonlinear Dynamics, vol. 39, pp. 79-94, 2005.
 T. Furuya, A. Tayaoka, M. Soeda, "Identification of Bilinear Systems by Wavelet Connection Coefficients", in Proc. SICE Annual Conference in Fukui, Fukui University, Japan, 2003, pp. 2158-2163.
 T. Binder, L. Blank, W. Dahmen, W. Marquardt, "Iterative Algorithms For Multiscale State Estimation, Part 2: Numerical Investigations", J. of Optimization Theory and Applications, vol. 111, no. 3, pp. 529-551, 2001.
 M. Garg and L. Dewan, "A Novel Method of Computing Haar Connection Coefficients for Analysis of HCI Systems", in Proc. of Second 2nd International Conference on Intelligent Human Computer Interaction (IHCI 2010), published in Lecture Notes in Control and Information Sciences (LNCS), Springer-Verlag, ISBN 978-81-8489-540-7, 2010, pp. 360-365. (To be cited on www.springerlink.com)
 J.L Wu, C.H. Chen, C.F. Chen, "A Unified Derivation of Operational Matrices of Integration for Integration in System Analysis", in IEEE Proc. Int. Conf. on Information Technology: Coding and Computing, 2000, pp. 436-442.