Lyapunov learning algorithm for Quasi-ARX neural network to identification of nonlinear dynamical system

IEEJ Transactions Elec Engng

Marhaban

et al. 2015

Self Cite

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.

“…Consider a single‐input, single‐output (SISO), black‐box, time‐invariant system whose input–output relationship is described by the following:

\begin{matrix} eqnarrayleft center right \\ eqnarray-1 y (t) & eqnarray-2 = & eqnarray-3 g (φ (t)) \end{matrix}

\begin{matrix} eqnarrayleft center right \\ eqnarray-1 y (t) & eqnarray-2 = & eqnarray-3 φ^{T} (t) ℵ (ξ (t)) . \end{matrix}

Section: Quasi‐arx Neural Network Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

IEEJ Transactions Elec Engng

Marhaban

et al. 2015

Self Cite

“…Through performing Taylor series expansions , the nonlinear continuous function can be presented as

\begin{matrix} eqnarrayleft center right \\ eqnarray-1 y (t) & eqnarray-2 = & eqnarray-3 y_{0} + φ {(t)}^{T} ℵ (φ (t)) \end{matrix}

where

are the Taylor coefficients;

denotes the input vector with elements

and n y represent the orders of time delay in the input–output data.

denotes a kernel function that is used to give the coefficients of the input vector.…”

Section: Control Strategymentioning

confidence: 99%

“…These also can be executed by neurofuzzy, wavelet, radial basis function, and multilayer perceptron neural network (MLPNN) . 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 .…”

Section: Introductionmentioning

confidence: 99%

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

IEEJ Transactions Elec Engng

Sutrisno

2015

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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.

“…The coefficients called as state dependent parameters estimation (SDPE) that consists of two parts: linear parameters and nonlinear parameters. The linear parameters estimator is performed by least square error (LSE) algorithm, which is set as bias vector for the output nodes of MLPNN [9], [10], [11]. 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).…”

Section: Introductionmentioning

confidence: 99%

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

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

Sutrisno

et al. 2014

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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.