A Generalized Approach for State Analysis and Parameter Estimation of Bilinear Systems using Haar Connection Coefficients
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.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] 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.
[8] 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.
[9] J. Rico, G. T. Heydt, "Parameter Estimation using an Orthogonal Series
Expansion", J. Electric Machines and Power Systems, vol. 28, pp. 761-
777, 2000.
[10] 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.
[11] 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.
[12] I. Daubechies, "The Wavelet Transform, Time-Frequency Localization
and Signal Analysis", IEEE Trans. Infor. Theory, vol. 36, pp. 961-1005,
1990.
[13] 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.
[14] Jer-Nan Juang, "Continuous-Time Bilinear System Identification", Nonlinear
Dynamics, vol. 39, pp. 79-94, 2005.
[15] 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.
[16] 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.
[17] 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)
[18] 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.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] 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.
[8] 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.
[9] J. Rico, G. T. Heydt, "Parameter Estimation using an Orthogonal Series
Expansion", J. Electric Machines and Power Systems, vol. 28, pp. 761-
777, 2000.
[10] 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.
[11] 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.
[12] I. Daubechies, "The Wavelet Transform, Time-Frequency Localization
and Signal Analysis", IEEE Trans. Infor. Theory, vol. 36, pp. 961-1005,
1990.
[13] 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.
[14] Jer-Nan Juang, "Continuous-Time Bilinear System Identification", Nonlinear
Dynamics, vol. 39, pp. 79-94, 2005.
[15] 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.
[16] 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.
[17] 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)
[18] 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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:63943", author = "Monika Garg and Lillie Dewan", title = "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.", keywords = "Bilinear Systems, Haar Wavelet, Haar ConnectionCoefficients, Parameter Estimation, Singular Bilinear Systems, StateAnalysis.", volume = "5", number = "3", pages = "495-6", }
