A bibliography on nonlinear system identification

Giannakis, Georgios B.; Serpedin, Erchin

doi:10.1016/s0165-1684(00)00231-0

Cited by 188 publications

(70 citation statements)

References 864 publications

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“…However, there are many practical situations, e.g., in communications and biomedical engineering, where the nonlinear processing of signals is needed. See extensive bibliography [1] devoted to the theory of nonlinear systems. Unlike the case of linear systems which can be uniquely identified by their impulse response, there is a wide variety of representations to characterize nonlinear systems, ranging from higher-order statistics, e.g., [2], [3], to series expansion methods, e.g., [4], [5].…”

mentioning

confidence: 99%

Online Prediction of Time Series Data With Kernels

Richard

Bermudez

Honeiné

2009

IEEE Trans. Signal Process.

423

348

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Abstract-Kernel-based algorithms have been a topic of considerable interest in the machine learning community over the last ten years. Their attractiveness resides in their elegant treatment of nonlinear problems. They have been successfully applied to pattern recognition, regression and density estimation. A common characteristic of kernel-based methods is that they deal with kernel expansions whose number of terms equals the number of input data, making them unsuitable for online applications. Recently, several solutions have been proposed to circumvent this computational burden in time series prediction problems. Nevertheless, most of them require excessively elaborate and costly operations. In this paper, we investigate a new model reduction criterion that makes computationally demanding sparsification procedures unnecessary. The increase in the number of variables is controlled by the coherence parameter, a fundamental quantity that characterizes the behavior of dictionaries in sparse approximation problems. We incorporate the coherence criterion into a new kernel-based affine projection algorithm for time series prediction. We also derive the kernel-based normalized LMS algorithm as a particular case. Finally, experiments are conducted to compare our approach to existing methods.

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confidence: 99%

Online Prediction of Time Series Data With Kernels

Richard

Bermudez

Honeiné

2009

IEEE Trans. Signal Process.

423

348

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“…(21,22) only stabilizes the angular velocity of the system. Once the angular velocity of the system is sufficiently close to zero, the desired angular velocity trajectory ω d (t) is augmented with a damping term so that the system's attitude converges to the desired attitude:…”

Section: Design Of the Desired Mrp Trajectorymentioning

confidence: 99%

“…However, the captured asteroid's physical parameters could be precisely estimated using online system identification techniques. 20, 21,22,23,24 Strategies for initial approach, inertial hovering, and body-fixed hovering are discussed in Refs. 25,26,27.…”

Section: Introductionmentioning

confidence: 99%

Attitude Control and Stabilization of Spacecraft with a Captured Asteroid

Bandyopadhyay

Chung

Hadaegh

2015

AIAA Guidance, Navigation, and Control Conference

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Administration's Asteroid Redirect Mission (ARM) aims to capture a Near Earth Orbit (NEO) asteroid or a piece of a large asteroid and transport it to the Earth-Moon system. In this paper, we provide a detailed analysis of one of the main control challenges for the first ARM mission concept, namely despinning and three-axis stabilizing the asteroid and spacecraft combination after the ARM spacecraft captures the tumbling NEO asteroid. We first show that control laws, which explicitly use the dynamics of the system in their control law equation, encounter a fundamental limitation due to modeling uncertainties. We show that in the presence of large modeling uncertainties, the resultant disturbance torque for such control laws may well exceed the maximum control torque of the conceptual ARM spacecraft. We then numerically compare the performance of three viable control laws: the robust nonlinear tracking control law, the adaptive nonlinear tracking control law, and the simple derivative plus proportional-derivative linear control strategy. We conclude that under very small modeling uncertainties, which can be achieved using online system identification, the robust nonlinear tracking control law guarantees exponential convergence to the fuel-optimal reference trajectory and hence consumes the least fuel. On the other hand, in the presence of large modeling uncertainties, measurement errors, and actuator saturations, the best strategy for stabilizing the asteroid and spacecraft combination is to first despin the system using a derivative (rate damping) linear control law and then stabilize the system in the desired orientation using the simple proportional-derivative linear control law. Moreover, the fuel consumed by the conceptual ARM spacecraft using these control strategies is upper bounded by 300 kg for the nominal range of NEO asteroid parameters. We conclude this paper with specific design guidelines for the ARM spacecraft for efficiently stabilizing the tumbling NEO asteroid and spacecraft combination. = Inertia matrices in Euler-Lagrangian formulation P(·) = Height of the power spectral density of the white noise= Center of mass of the ARM spacecraft S O = Base of the ARM-spacecraft's body

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“…The Hammerstein system ( Fig. 1) is the simplest structure of this kind and hence it is mostly considered in the system identification literature (see, e.g., (Giannakis and Serpedin, 2001;Haber and Keviczky, 1999) for the bibliography). It is built of a static nonlinearity μ( ) and linear dynamics, with the impulse response {γ i } ∞ i=0 , connected in a cascade and described by the following set of equations:…”

Section: Introductionmentioning

confidence: 99%

Generalized Kernel Regression Estimate for the Identification of Hammerstein Systems

Mzyk¹

2007

International Journal of Applied Mathematics and Computer Science

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A modified version of the classical kernel nonparametric identification algorithm for nonlinearity recovering in a Hammerstein system under the existence of random noise is proposed. The assumptions imposed on the unknown characteristic are weak. The generalized kernel method proposed in the paper provides more accurate results in comparison with the classical kernel nonparametric estimate, regardless of the number of measurements. The convergence in probability of the proposed estimate to the unknown characteristic is proved and the question of the convergence rate is discussed. Illustrative simulation examples are included.

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A bibliography on nonlinear system identification

Cited by 188 publications

References 864 publications

Online Prediction of Time Series Data With Kernels

Online Prediction of Time Series Data With Kernels

Attitude Control and Stabilization of Spacecraft with a Captured Asteroid

Generalized Kernel Regression Estimate for the Identification of Hammerstein Systems

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