Adaptive Regulator for Hammerstein and Wiener Systems With Noisy Observations

Chen, Han-Fu

doi:10.1109/tac.2007.894536

Cited by 19 publications

(9 citation statements)

References 16 publications

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“…We first note that J ∩ S(0) {u 0 } is a singleton by Lemma 6. By Lemma 1 in Chen (2007), if lim k→∞ u i,k = u i , then lim k→∞ y i,k = h i (u i ). Therefore, to prove (111) it suffices to show that d(u k , J ∩…”

Section: Similar Tomentioning

confidence: 97%

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Output Consensus of Networked Hammerstein and Wiener Systems

Feng¹,

Chen²

2019

SIAM J. Control Optim.

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In this paper we consider the output consensus problem of networked Hammerstein and Wiener systems in a noisy environment. The Hammerstein or Wiener system is assumed to be open-loop stable, and its static nonlinearity is allowed to grow up but not faster than a polynomial. A control algorithm based on the distributed stochastic approximation algorithm with expanding truncations is designed and it is shown that under the designed control the output consensus is achieved. The numerical simulation given in the paper justifies the theoretical assertions.

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Section: Similar Tomentioning

confidence: 97%

“…Noticing the choice of step-size and truncation bound, similar to Lemma 2 in Chen (2007) we have the following lemma.…”

Section: Properties Of Noisesmentioning

confidence: 99%

Output Consensus of Networked Hammerstein and Wiener Systems

Feng¹,

Chen²

2019

SIAM J. Control Optim.

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“…In some earlier contributions [17][18][19], adaptive controllers are studied only through some numerical examples. Later, the contributions [20][21][22][23][24][25][26][27][28][29][30] have presented some elegant adaptive control algorithms together with rigorous theoretical analysis. Although many interesting results have been generated, most of these studies suffer from one or more of the following drawbacks, which narrow the applications of the results: the linear subsystem is of minimum phase, the disturbance is subject to Gaussian white noise, and the effect of unmodeled dynamics is neglected.…”

Section: Introductionmentioning

confidence: 99%

Robust adaptive control of Hammerstein nonlinear systems and its application to typical CSTR problems

Zhang

Mao

2016

Adaptive Control & Signal

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This paper considers the robust adaptive control of Hammerstein nonlinear systems with uncertain parameters. The control scheme is derived from a modified criterion function which can overcome non-minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. An online pole assignment technique is also presented to guarantee that Assumption 2 always holds. Rigorous theoretical analysis indicates that the parameter estimation convergence and the closed-loop system stability can be guaranteed under mild conditions. Simulation examples including two typical continuous stirred tank reactor problems are studied to verify the effectiveness of the control scheme. ROBUST ADAPTIVE CONTROL OF HAMMERSTEIN NONLINEAR SYSTEMS 165 where f i .u.t // are user-chosen basis functions. This work employs the following polynomial basis functions to approximate the static nonlinearities Figure 2. Adaptive control scheme for Hammerstein system. The initialization is that O Â.0/ D OE1:4; 0:12; 0:8; 0:1; 0:35; 0:7; 0:05; 0:2 T y.0/ D v.0/ D u.0/ D 0, P .0/ D 10 5 I , $ D 0:75, D 0:02 for noise-free case or D 0:1 for noisy case. Simulations are conducted under the following initial conditions: Condition 1 x 3 .0/ D 0:8467; x 4 .0/ D 1:3796; y R .0/ D x 5 .0/ D 1:2737; u Q .0/ D 0 Condition 2. x 3 .0/ D 1; x 4 .0/ D 0:3796; y R .0/ D x 5 .0/ D 0:7737; u Q .0/ D 0

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“…In Chen (2007), Ding, Chen, and Iwai (2007), Figueroa, Cousseau, Werner, and Laakso (2007), Kung and Womack (1983), Pajunen (1992), and Zhao and Chen (2009), adaptive controllers are studied 2 B. Zhang et al…”

Section: Introductionmentioning

confidence: 99%

“…Up to now, the over-parameterized method has been used successfully as recursive estimator in adaptive control for H and W systems (Chen, 2007;Figueroa et al, 2007;Kung & Womack, 1983;Pajunen, 1992;Zhao & Chen, 2009). In these contributions, blockoriented models (only H and W systems considered) are parameterized to be bilinear models.…”

Section: Introductionmentioning

confidence: 99%

Adaptive control of Hammerstein–Wiener nonlinear systems

Zhang

Hong

Mao

2014

International Journal of Systems Science

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The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.

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Adaptive Regulator for Hammerstein and Wiener Systems With Noisy Observations

Cited by 19 publications

References 16 publications

Output Consensus of Networked Hammerstein and Wiener Systems

Output Consensus of Networked Hammerstein and Wiener Systems

Robust adaptive control of Hammerstein nonlinear systems and its application to typical CSTR problems

Adaptive control of Hammerstein–Wiener nonlinear systems

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