Recursive Identification and Parameter Estimation

Chen, Han-Fu; Zhao, Wenxiao

doi:10.1201/b17078

Cited by 26 publications

(18 citation statements)

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“…In addition, we do not require the observation noise to be an MDS as in [13]. As shown in [36], [37], A5 is probably the weakest requirement for the noise since it is also necessary for convergence whenever the root x 0 of f (·) is a singleton and f (·) is continuous at x 0 . Compared with the random communication graphs used in [13], here we use the deterministic switching graphs to describe the communication relationships among agents.…”

Section: Resultsmentioning

confidence: 99%

“…In Corollary 5.1 "non-convergence of X k to zero" is assumed rather than proved, but the numerical simulations substantiate this assertion. This is not surprising because if we compare (62) with u (i) k given in [37], the estimates for unit eigenvectors corresponding to eigenvalues arranged in the decreasing order of a noisy observed matrix A (pp. 289-316 in [37]), we find that (62) and the recursive expression ((5.1.9) of [37]) of u (1) k are in a complete similarity while the latter converges to the unit eigenvector corresponding to the largest eigenvalue of A as proved in [37].…”

Section: A Distributed Pcamentioning

confidence: 93%

“…This is not surprising because if we compare (62) with u (i) k given in [37], the estimates for unit eigenvectors corresponding to eigenvalues arranged in the decreasing order of a noisy observed matrix A (pp. 289-316 in [37]), we find that (62) and the recursive expression ((5.1.9) of [37]) of u (1) k are in a complete similarity while the latter converges to the unit eigenvector corresponding to the largest eigenvalue of A as proved in [37]. It is worth noting that normalization technique used in [37] automatically excludes estimates from tending to zero, but this can also be achieved by truncations as done in [36, Section 6.2] when solving the adaptive stabilization problem, where not only the upper side truncations are used to prevent estimates from diverging to infinity but also the lower side truncations for estimates not tending to zero.…”

Section: A Distributed Pcamentioning

confidence: 93%

“…This work was supported by the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences. and adaptive control, see, e.g., [35]- [37]. Recently, many distributed problems are also solved by SA-based distributed algorithms, e.g., distributed parameter estimation [3], [10], distributed convex optimization over random networks [17], and distributed non-convex stochastic optimization [18].…”

Section: Introductionmentioning

confidence: 99%

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Distributed Stochastic Approximation Algorithm With Expanding Truncations

Lei¹,

Chen

2020

IEEE Trans. Automat. Contr.

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In this work, a novel distributed stochastic approximation algorithm (DSAA) is proposed to seek roots of the sum of local functions, each of which is associated with an agent from the multiple agents connected over a network. At each iteration, each agent updates its estimate for the root utilizing the noisy observations of its local function and the information derived from the neighboring agents. The key difference of the proposed algorithm from the existing ones consists in the expanding truncations (so it is called as DSAAWET), by which the boundedness of the estimates can be guaranteed without imposing the growth rate constraints on the local functions. The estimates generated by DSAAWET are shown to converge almost surely (a.s.) to a consensus set, which belongs to a connected subset of the root set of the sum function. In comparison with the existing results, we impose weaker conditions on the local functions and on the observation noise. We then apply the proposed algorithm to two applications, one from signal processing and the other one from distributed optimization, and establish the almost sure convergence. Numerical simulation results are also included.

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Section: Resultsmentioning

confidence: 99%

Section: A Distributed Pcamentioning

confidence: 93%

Section: A Distributed Pcamentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Distributed Stochastic Approximation Algorithm With Expanding Truncations

Lei¹,

Chen

2020

IEEE Trans. Automat. Contr.

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“…It is an acceptable and reasonable claim for this study that the other well-known recursive computational algorithms such as Kalman Filters, Bayesian estimation mechanism, and so on could be applicable after properly revised/extended from their standard formulations. It is generally accepted that recursive algorithms are particularly important for real time adaptive control and other real time systems (Chen and Zhao 2014). 2) To support justification 1, Kalman Filter is selected.…”

Section: Introductionmentioning

confidence: 99%

An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models

Zhu

Zhao

2016

International Journal of Systems Science

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Abstract:In this study an enhanced Kalman Filter formulation for linear in the parameters models with inherent correlated errors is proposed to build up a new framework for nonlinear rational model parameter estimation. The mechanism of Linear Kalman Filter (LKF) with point data processing is adopted to develop a new recursive algorithm. The novelty of the Enhanced Linear Kalman Filter (EnLKF in short and distinguished from Extended Kalman Filter (EKF)) is that it is not formulated from the routes of extended Kalman Filters (to approximate nonlinear models by linear approximation around operating points through Taylor expansion) and also it includes LKF as its subset while linear models have no correlated errors in regressor terms. No matter linear or nonlinear models in representing a system from measured data, it is very common to have correlated errors between measurement noise and regression terms, the EnLKF provides a general solution for unbiased model parameter estimation without extra cost to convert model structure. The associated convergence is analysed to provide a quantitative indicator for applications and reference for further research. Three simulated examples are selected to bench-test the performance of the algorithm. In addition, the style of conducting numerical simulation studies provides a user-friendly step by step procedure for the readers/users with interest in their ad hoc applications. It should be noted that this approach is fundamentally different from those using linearization to approximate nonlinear models and then conduct state/parameter estimate.

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Identification for Wiener‐Hammerstein systems under quantized inputs and quantized output observations

Guo

Zhao

2019

Asian Journal of Control

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This paper investigates the Wiener‐Hammerstein system identification with quantized inputs and quantized output observations. By parameterizing the static nonlinear function, system identifiability is discussed first. Then, for the identifiable system a three‐step algorithm is proposed to estimate the unknown parameters by employing the empirical measure‐based method and the quasi‐convex combination technique. Finally, the algorithm is proved to be strongly convergent, the mean‐square convergence rate is presented, and the asymptotic efficiency is given by selecting a suitable transformation matrix. A numerical simulation is included to demonstrate the main results obtained.

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Recursive Identification and Parameter Estimation

Cited by 26 publications

References 0 publications

Distributed Stochastic Approximation Algorithm With Expanding Truncations

Distributed Stochastic Approximation Algorithm With Expanding Truncations

An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models

Identification for Wiener‐Hammerstein systems under quantized inputs and quantized output observations

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