Estimation of IIR Systems with Binary-Valued Observations

Abstract

Estimation and control problems with binary-valued observations exist widely in practical systems. However, most of the related works are devoted to finite impulse response (FIR for short) systems, and the theoretical problem of infinite impulse response (IIR for short) systems has been less explored. To study the estimation problems of IIR systems with binary-valued observations, the authors introduce a projected recursive estimation algorithm and analyse its global convergence properties, by using the stochastic Lyapunov function methods and the limit theory on double array martingales. It is shown that the estimation algorithm has similar convergence results as those for FIR systems under a weakest possible non-persistent excitation condition. Moreover, the upper bound for the accumulated regret of adaptive prediction is also established without resorting to any excitation condition.

Keywords

Binary-valued observations / Infinite impulse response / Adaptive estimation / Double array martingales / Adaptive prediction

References

[1] Bottegal G, Hjalmarsson H, Pillonetto G. A new kernel-based approach to system identification with quantized output data. Automatica, 2017, 85: 145-152

[2] Chen H F, Guo L. Identification and Stochastic Adaptive Control, 1991, Boston: Birkhauser

[3] Ghysen A. The origin and evolution of the nervous system. Int. J. Dev. Biol., 2003, 47(7–8): 555-562

[4] Guo J, Zhao Y. Recursive projection algorithm on FIR system identification with binary-valued observations. Automatica, 2013, 49(11): 3396-3401

[5] Guo L. Convergence and logarithm laws of self-tuning regulators. Automatica, 1995, 31(3): 435-450

[6] Guo L, Huang D W, Hannan E J. On ARX(∞) approximation. J. Multivar. Anal, 1990, 32(1): 17-47

[7] Huang D, Guo L. Estimation of nonstationary ARMAX models based on the Hannan-Rissanen method. Ann. Stat., 1990, 18(4): 1729-1756

[8] Lai T L, Wei C Z. Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann. Stat., 1982, 10(1): 154-166

[9] Marelli D, You K, Fu M. Identification of ARMA models using intermittent and quantized output observations. Automatica, 2013, 49(2): 360-369

[10] Schwiebert L, Wang L Y. Robust control and rate coordination for efficiency and fairness in ABR traffic with explicit rate marking. Comput. Commun., 2001, 24(13): 1329-1340

[11] Song Q. Recursive identification of systems with binary-valued outputs and with ARMA noises. Automatica, 2018, 93: 106-113

[12] Sun J, Yong W K, Wang L Y. Aftertreatment control and adaptation for automotive lean burn engines with HEGO sensors. Int. J. Adapt. Control Signal Process., 2004, 18(2): 145-166

[13] Wang J, Zhang Q. Identification of FIR systems based on quantized output measurements: A quadratic programming-based method. IEEE Trans. Autom. Control, 2014, 60(5): 1439-1444

[14] Wang L Y, Zhang J F, Yin G G. System identification using binary sensors. IEEE Trans. Autom. Control, 2003, 48(11): 1892-1907

[15] Zhang H, Wang T, Zhao Y. Asymptotically efficient recursive identification of FIR systems with binary-valued observations. IEEE Trans. Syst. Man Cybern. -Syst., 2021, 51(5): 2687-2700

[16] Zhang, L. and Guo, L., Adaptive identification with guaranteed performance under saturated-observation and non-persistent excitation, 2022, https://arxiv.org/abs/2207.02422.

[17] Zhang L, Zhao Y, Guo L. Identification and adaptation with binary-valued observations under non-persistent excitation condition. Automatica, 2022, 138: 110158

[18] Zhao W X, Chen H F. Markov chain approach to identifying Wiener systems. Sci. China Inf. Sci., 2012, 55(5): 1201-1217

[19] Zhao Y L, Wang L Y, Yin G G, Zhang J F. Identification of Wiener systems with binary-valued output observations. Automatica, 2007, 43(10): 1752-1765