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Online Identification of Stochastic Continuous-Time Wiener Models Using Sampled Data
Published 9 Mar 2024 in stat.ME, cs.LG, cs.SY, eess.SP, and eess.SY | (2403.05899v1)
Abstract: It is well known that ignoring the presence of stochastic disturbances in the identification of stochastic Wiener models leads to asymptotically biased estimators. On the other hand, optimal statistical identification, via likelihood-based methods, is sensitive to the assumptions on the data distribution and is usually based on relatively complex sequential Monte Carlo algorithms. We develop a simple recursive online estimation algorithm based on an output-error predictor, for the identification of continuous-time stochastic parametric Wiener models through stochastic approximation. The method is applicable to generic model parameterizations and, as demonstrated in the numerical simulation examples, it is robust with respect to the assumptions on the spectrum of the disturbance process.
- P. Hammond, Theory of self-adaptive control systems. Springer, 1965.
- P. Eykhoff, System Identification. Parameter and State Estimation. John Wiley, 1974.
- P. C. Young, Recursive estimation and time-series analysis: An introduction for the student and practitioner. Springer Science & Business Media, 2011.
- G. Goodwin and K. Sin, Adaptive Filtering Prediction and Control. Dover Books on Electrical Engineering, Dover Publications, 2014.
- H.-F. Chen and W. Zhao, Recursive identification and parameter estimation. CRC Press, 2014.
- L. Ljung and T. Söderström, Theory and practice of recursive identification. MIT press, 1983.
- L. Ljung, System Identification: Theory for the User. Prentice Hall, 2nd ed., 1999.
- Prentice Hall, 1989.
- J. Olsson and J. Westerborn Alenlöv, “Particle-based online estimation of tangent filters with application to parameter estimation in nonlinear state-space models,” Annals of the Institute of Statistical Mathematics, vol. 72, pp. 545–576, 2020.
- N. Kantas, A. Doucet, S. S. Singh, J. Maciejowski, and N. Chopin, “On particle methods for parameter estimation in state-space models,” Statist. Sci., vol. 30, no. 3, pp. 328–351, 2015.
- H. Singer, Langevin and Kalman Importance Sampling for Nonlinear Continuous-Discrete State-Space Models. Springer, 2018.
- A. Beskos, D. Crisan, A. Jasra, N. Kantas, and H. Ruzayqat, “Score-based parameter estimation for a class of continuous-time state space models,” SIAM Journal on Scientific Computing, vol. 43, no. 4, pp. A2555–A2580, 2021.
- S. C. Surace and J.-P. Pfister, “Online maximum-likelihood estimation of the parameters of partially observed diffusion processes,” IEEE Transactions on Automatic Control, vol. 64, no. 7, pp. 2814–2829, 2018.
- M. Abdalmoaty, H. Hjalmarsson, and B. Wahlberg, “The Gaussian Maximum-Likelihood Estimator Versus the Optimally Weighted Least-Squares Estimator [Lecture Notes],” IEEE Signal Processing Magazine, vol. 37, no. 6, pp. 195–199, 2020.
- S. Oymak and N. Ozay, “Non-asymptotic identification of LTI systems from a single trajectory,” in 2019 American Control Conference (ACC), pp. 5655–5661, IEEE, 2019.
- M. Simchowitz, K. Singh, and E. Hazan, “Improper learning for non-stochastic control,” in Conference on Learning Theory, pp. 3320–3436, PMLR, 2020.
- N. Matni and S. Tu, “A tutorial on concentration bounds for system identification,” in 2019 IEEE 58th Conference on Decision and Control (CDC), pp. 3741–3749, IEEE, 2019.
- Y. Li, T. Zhang, S. Das, J. Shamma, and N. Li, “Non-asymptotic system identification for linear systems with nonlinear policies,” arXiv preprint arXiv:2306.10369, 2023.
- D. Foster, T. Sarkar, and A. Rakhlin, “Learning nonlinear dynamical systems from a single trajectory,” in Learning for Dynamics and Control, pp. 851–861, PMLR, 2020.
- H. Mania, M. I. Jordan, and B. Recht, “Active learning for nonlinear system identification with guarantees,” arXiv preprint arXiv:2006.10277, 2020.
- London: Springer London, 2010.
- S. Boyd and L. Chua, “Fading memory and the problem of approximating nonlinear operators with Volterra series,” IEEE Transactions on Circuits and Systems, vol. 32, pp. 1150–1161, Nov 1985.
- T. Wigren, “Recursive prediction error identification using the nonlinear Wiener model,” Automatica, vol. 29, no. 4, pp. 1011 – 1025, 1993.
- T. Wigren, “Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model,” IEEE Transactions on Automatic Control, vol. 39, no. 11, pp. 2191–2206, 1994.
- T. Wigren, “Recursive identification of a nonlinear state space model,” International Journal of Adaptive Control and Signal Processing, vol. 37, no. 2, pp. 447–473, 2023.
- M. Abdalmoaty and H. Hjalmarsson, “Linear prediction error methods for stochastic nonlinear models,” Automatica, vol. 105, pp. 49–63, 2019.
- M. Abdalmoaty and H. Hjalmarsson, “Application of a linear PEM estimator to a stochastic Wiener-Hammerstein benchmark problem,” IFAC-PapersOnLine, vol. 51, no. 15, pp. 784 – 789, 2018.
- R. Bereza, O. Eriksson, M. R.-H. Abdalmoaty, D. Broman, and H. Hjalmarsson, “Stochastic approximation for identification of non-linear differential-algebraic equations with process disturbances,” in 2022 IEEE 61st Conference on Decision and Control (CDC), pp. 6712–6717, IEEE, 2022.
- H. Robbins and S. Monro, “A stochastic approximation method,” Ann. Math. Statist., vol. 22, pp. 400–407, 09 1951.
- K. J. Åström, Introduction to Stochastic Control Theory. Mathematics in Science and Engineering, Academic Press, 1970.
- L. Ljung, “Strong convergence of a stochastic approximation algorithm,” The Annals of Statistics, vol. 6, no. 3, pp. 680–696, 1978.
- J. E. Hutton and P. I. Nelson, “Interchanging the order of differentiation and stochastic integration,” Stochastic processes and their applications, vol. 18, no. 2, pp. 371–377, 1984.
- C. Minto, T. Schnider, T. Short, K. Gregg, A. Gentilini, and S. Shafer, “Response Surface Model for Anesthetic Drug Interactions,” Anesthesiology, vol. 92, pp. 1603–1616, 06 2000.
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