Deep searching for parameter estimation of the linear time invariant (LTI) system by using Quasi-ARX neural network

In this paper, a new switching mechanism is proposed based on the state of dynamic tracking error so that more information will be provided –not only the error but also a one up to pth differential error will be available as the switching variable. The switching index is based on the Lyapunov stability theory. Thus the switching mechanism can work more effectively and efficiently. A simplified quasi‐ARX neural‐network (QARXNN) model presented by a state‐dependent parameter estimation (SDPE) is used to derive the controller formulation to deal with its computational complexity. The switching works inside the model by utilizing the linear and nonlinear parts of an SDPE. First, a QARXNN is used as an estimator to estimate an SDPE. Second, by using SDPE, the state of dynamic tracking error is calculated to derive the switching index. Additionally, the switching formula can use an SDPE as the switching variable more easily. Finally, numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance‐rejection performances. Experimental results demonstrate its effectiveness. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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“…The details of the algorithm of the QARXNN model can be found in Refs . A QARXNN model with an MLPNN set as an embedded system is shown in Fig.…”

Section: Quasi‐arx Neural Network Modelmentioning

confidence: 99%

Quasi‐ARX neural network based adaptive predictive control for nonlinear systems

Jami'in

Marhaban

et al. 2015

IEEJ Transactions Elec Engng

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“…By performing Taylor series expansion, we develop the nonlinear system presented as a linear correlation between the input vector and its coefficients. If the system modeling represents a plant that is a linear system, the coefficients obtained will be constant; otherwise, if the system modeling represents a plant that is a nonlinear system, the obtained coefficients will be a function of time . A QARXNN model puts nonlinear function into the coefficients of input vector as follows:

\begin{matrix} eqnarrayleft center right \\ eqnarray-1 y (t, φ (t)) = b_{(1, t)} u (t - 1) + \dots + b_{(n_{u}, t)} u (t - n_{u}) & eqnarray-2 & eqnarray-3 \\ eqnarray-1 - a_{(1, t)} y (t - 1) - \dots - a_{(n_{y}, t)} y (t - n_{y}) & eqnarray-2 & eqnarray-3 \end{matrix}

Figure illustrates the scheme of system identification and prediction by QARXNN model.…”

Section: Control Strategymentioning

confidence: 99%

“…If the model in is sufficient to model the input–output training data of the system, Assumption 1 and Assumption 2 are fulfilled, and then the output at ( t + d ) can be predicted. To obtain the predicted output, is regressed at time ( t + d ) described as

\begin{matrix} eqnarrayleft center right \\ eqnarray-1 & eqnarray-2 & eqnarray-3 y (t + d) = {\hat{b}}_{(1, t + d)} u (t + d - 1) + \dots + \\ eqnarray-1 & eqnarray-2 & eqnarray-3 {\hat{b}}_{(n_{u}, t + d)} u (t - n_{u} + d) - â_{(1, t + d)} y (t - 1 + d) \\ eqnarray-1 & eqnarray-2 & eqnarray-3 - \dots - â_{(n_{y}, t + d)} y (t - n_{y} + d) \end{matrix}

where φ ( t + d ) = [ y ( t + d − 1) y ( t + d − 2)⋯ y ( t + d − n y ) u ( t + d − 1) u ( t + d − 2)⋯ u ( t + d − n u )] T is d step ahead of the input vector.

\overset{ℵ}{true} (φ (t + d))

and

{[â_{(1, t + d)} \dots â_{(n_{y}, t + d)} {\overset{b}{true}}_{(1, t + d)} \dots {\overset{b}{true}}_{(n_{u}, t + d)}]}^{T}

are the estimated parameters of the nonlinear part by MLPNN and its elements, respectively.…”

Section: Control Strategymentioning

confidence: 99%

“…The accuracy, stability, and the speed of convergence can be improved with Lyapunov training . The QARXNN can also be used to identify the linear system with more accurate results than those achieved by using the technique of recursive least squares error identification . The contributions of this paper are as follows: (i) the modeling of WECS with uncertainty parameters is derived by wind speed signal under an autoregressive moving average (ARMA) model with random process; (ii) a QARXNN is applied to model and predict WECS dynamics online with emphasis on the search parameters of the input vector; (iii) with the minimum variance controller law, a controller signal is derived by QARXNN prediction model using linear and nonlinear parameters with the switching.…”

Section: Introductionmentioning

confidence: 99%

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Maximum power tracking control for a wind energy conversion system based on a quasi‐ARX neural network model

Jami'in

Sutrisno

2015

IEEJ Transactions Elec Engng

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By itself, a wind turbine is already a fairly complex system with highly nonlinear dynamics. Changes in wind speed can affect the dynamic parameters of wind turbines, thus rendering the parameters uncertain. However, we can identify the dynamics of the wind energy conversion system (WECS) online by a quasi‐ARX neural network (QARXNN) model. A QARXNN presents a problem in searching for the coefficients of the regression vector (input vector). A multilayer perceptron neural network (MLPNN) is an embedded system that provides the unknown parameters used to parameterize the input vector. Fascinatingly, the coefficients of the input vector from prediction model can be set as controller parameters directly. The stability of the closed‐loop controller is guaranteed by the switching of the linear and nonlinear parts of the parameters. The dynamic of WECS is derived with given parameters, and then a wind speed signal created by a random model is fed to the system causing uncertainty parameters and reducing the power that can be absorbed from wind. By using a minimum variance controller, the maximum power is tracked from WECS. From the simulation results, it is observed that the proposed controller is effective in tracking the maximum power of WECS. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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“…In view of a nonlinear system is modeled under a quasi-linear autoregressive (quasi-ARX) model, nonlinear nature is placed on to the coefficients of the autoregressive (AR) or autoregressive moving average (ARMA). If the system is linear than SDPE will converge at the fixed value, whereas if the system is nonlinear then SDPE is a variable that will change at any time [12]. In this paper, an adaptive control based QARXNN prediction model is proposed to control of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

An adaptive predictive control based on a quasi-ARX neural network model

Jami'in

Sutrisno

et al. 2014

2014 13th International Conference on Control Automation Robotics &Amp; Vision (ICARCV)

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A quasi-ARX (quasi-linear ARX) neural network (QARXNN) model is able to demonstrate its ability for identification and prediction highly nonlinear system. The model is simplified by a linear correlation between the input vector and its nonlinear coefficients. The coefficients are used to parameterize the input vector performed by an embedded system called as state dependent parameter estimation (SDPE), which is executed by multi layer parceptron neural network (MLPNN). SDPE consists of the linear and nonlinear parts. The controller law is derived via SDPE of the linear and nonlinear parts through switching mechanism. The dynamic tracking controller error is derived then the stability analysis of the closed-loop controller is performed based Lyapunov theorem. Linear based adaptive robust control and nonlinear based adaptive robust control is performed with the switching of the linear and nonlinear parts parameters based Lyapunov theorem to guarantee bounded and convergence error.

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Deep searching for parameter estimation of the linear time invariant (LTI) system by using Quasi-ARX neural network

Cited by 17 publications

References 28 publications

Quasi‐ARX neural network based adaptive predictive control for nonlinear systems

Quasi‐ARX neural network based adaptive predictive control for nonlinear systems

Maximum power tracking control for a wind energy conversion system based on a quasi‐ARX neural network model

An adaptive predictive control based on a quasi-ARX neural network model

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