A novel method is developed incorporating a special input sequence for a general class of observable and reachable bilinear system identification. An order reduction scheme is introduced to determine the system matrices. This method makes a significant improvement to its predecessors by removing the observability requirement for the linear part of the bilinear systems. Numerical examples are given to demonstrate the method developed in this paper.
BrockettR(1973) Lie algebras and Lie groups in control theory. In: MayneDQBrockettRW (eds) Geometric Methods in System Theory, Dordrecht, The Netherlands: D. Reidel Publishing Company, pp. 17–56.
2.
BruniCDiPilloGKochG (1971) On the mathematical models of bilinear systems. Automatica, 2(1): 11–26.
3.
BruniCDiPilloGKochG (1974) Bilinear systems: an appealing class of nearly linear systems in theory and application. IEEE Transactions on Automatic Control, 19: 334–348.
4.
ElliottDL(1999) Bilinear systems. In: WebsterJ (ed.) Encyclopedia of Electrical Engineering, Vol. II, New York: John Wiley and Sons, pp. 308–323.
5.
FeldmanMBucherIRotbergJ (2009) Experimental identification of nonlinearities under free and forced vibration using the Hilbert transform. Journal of Vibration and Control, 15(10): 1563–1579.
6.
GoodzeitNEPhanMQ (2000) A clear-box adaptive system for flexible spacecraft identification and disturbance rejection. Journal of Vibration and Control, 6: 757–780.
7.
GrasselliOMIsidoriA (1997) Deterministic state reconstruction and reachability of bilinear processes. Proceedings of IEEE joint automatic control conference, San Francisco, CA, pp. 1423–1427. June 1977.
8.
HaraSFurutaK (1973) Observability for bilinear systems. International Journal of Control, 26(4): 559–572.
9.
HwangYR (2001) On the reachability of continuous bilinear systems. Journal of the Chinese Iustitute of Engineers, 24(5): 635–639.
10.
IsidoriARubertiA(1973) Realization theory of bilinear systems. In: MayneDQBrockettRW (eds) Geometric Methods in System Theory, Dordrecht, The Netherlands: D. Reidel Publishing Company, pp. 83–130.
11.
JuangJ-N (1994) Applied System Identification, New Jersey: Prentice Hall.
12.
JuangJ-N (2005) Continuous-time bilinear system identification. Nonlinear Dynamics, 39(1–2): 79–94.
13.
JuangJ-N (2009) Generalized bilinear system identification. Journal of the Astronautical Sciences, 57(1–2): 261–273.
14.
JuangJ-NLeeC-H (2010) Continuous-time bilinear system identification using single experiment with multiple pulses. Nonlinear Dynamics, 69(3): 1009–1021. DOI 10.1007/s11071-011-0323-9.
15.
JuangJ-NPappaRS (1986) Effect of noise on modal parameters identified by the eigensystem realization algorithm. Journal of Guidance, Control, and Dynamics, 9(3): 294–303.
16.
JuangJ-NPhanMQ (2001) Identification and Control of Mechanical Systems, New York: Cambridge University Press.
17.
JuangJ-NCooperJEWrightJR (1988) An eigensystem realization algorithm using data correlations (ERA/DC) for modal parameter identification. Journal of Control Theory and Advanced Technology, 4(1): 5–14.
18.
JuangJ-NPhanMQHortaLG (1993) Identification of observer/Kalman filter Markov parameters: theory and experiments. Journal of Guidance, Control and Dynamics, 16(2): 320–329.
19.
LeeC-HJuangJ-H (2010) Nonlinear system identification – a continuous-time bilinear state space approach. In: Kyle T. Alfriend astrodynamics symposium, Monterey, CA: 18–19 May 2010, AAS 10-328.
20.
MajjiMJuangJ-NJunkinsJL (2009) Continuous-time bilinear system identification using repeated experiments. AAS/AIAA astrodynamics specialist conference,, Pittsburgh, Pennsylvania9–13 August 2009, AAS 09-366.
PachecoRPSteffenVJr (2002) Using orthogonal functions for identification and sensitivity analysis of mechanical systems. Journal of Vibration and Control, 8(7): 993–1021.
23.
PrazenicaRJKurdilaAJ (2004) Volterra Kernel identification using triangular wavelets. Journal of Vibration and Control, 10(4): 597–622.
24.
RughWJ (1981) Nonlinear System Theory: The Volterra/Wiener Approach, Baltimore, MD: Johns Hopkins University Press.
25.
SenP (1981) On the choice of input for observability in bilinear systems. IEEE Transactions on Automatic Control, 26: 451–454.
26.
SvoronosSStephanopoulosGArisR (1980) Bilinear approximation of general non-linear dynamic systems with linear inputs. International Journal of Control, 31(1): 109–126.
27.
WilliamsonD (1977) Observation of bilinear systems with application to biological control. Automatica, 13: 243–254.
