System Identification for Nonlinear Control Using Neural Networks

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memor

Global models of dynamic complex systems – modelling using the multilayer neural networks

In this paper, global models of dynamic complex systems using the neural networks isdiscussed. The description of a complex system is given by a description of each system elementand structure. As a model the multilayer neural networks with the tapped delay line (TDL), whichhave the same structure as a complex system, are accepted. Two approaches, a global model and aglobal model with the quality local model taken into account are proposed.To learn global models the modified back-propagation algorithms have been developed for theunique structure of the complex model. To model dynamic simple plants, of which the complexsystem is composed, a series-parallel model of identification using the feedforward network withthe tapped delay line (TDL) and the feedback loops, in which the gradient can be calculated bymeans of the simpler static back-propagation method is proposed. Computer simulations wereperformed for the dynamic complex system, which consists of two dynamic nonlinear simpleplants connected in series, described by means of nonlinear difference equations

Fuzzy jump wavelet neural network based on rule induction for dynamic nonlinear system identification with real data applications

Aim Fuzzy wavelet neural network (FWNN) has proven to be a promising strategy in the identification of nonlinear systems. The network considers both global and local properties, deals with imprecision present in sensory data, leading to desired precisions. In this paper, we proposed a new FWNN model nominated “Fuzzy Jump Wavelet Neural Network” (FJWNN) for identifying dynamic nonlinear-linear systems, especially in practical applications. Methods The proposed FJWNN is a fuzzy neural network model of the Takagi-Sugeno-Kang type whose consequent part of fuzzy rules is a linear combination of input regressors and dominant wavelet neurons as a sub-jump wavelet neural network. Each fuzzy rule can locally model both linear and nonlinear properties of a system. The linear relationship between the inputs and the output is learned by neurons with linear activation functions, whereas the nonlinear relationship is locally modeled by wavelet neurons. Orthogonal least square (OLS) method and genetic algorithm (GA) are respectively used to purify the wavelets for each sub-JWNN. In this paper, fuzzy rule induction improves the structure of the proposed model leading to less fuzzy rules, inputs of each fuzzy rule and model parameters. The real-world gas furnace and the real electromyographic (EMG) signal modeling problem are employed in our study. In the same vein, piecewise single variable function approximation, nonlinear dynamic system modeling, and Mackey–Glass time series prediction, ratify this method superiority. The proposed FJWNN model is compared with the state-of-the-art models based on some performance indices such as RMSE, RRSE, Rel ERR%, and VAF%. Results The proposed FJWNN model yielded the following results: RRSE (mean±std) of 10e-5±6e-5 for piecewise single-variable function approximation, RMSE (mean±std) of 2.6–4±2.6e-4 for the first nonlinear dynamic system modelling, RRSE (mean±std) of 1.59e-3±0.42e-3 for Mackey–Glass time series prediction, RMSE of 0.3421 for gas furnace modelling and VAF% (mean±std) of 98.24±0.71 for the EMG modelling of all trial signals, indicating a significant enhancement over previous methods. Conclusions The FJWNN demonstrated promising accuracy and generalization while moderating network complexity. This improvement is due to applying main useful wavelets in combination with linear regressors and using fuzzy rule induction. Compared to the state-of-the-art models, the proposed FJWNN yielded better performance and, therefore, can be considered a novel tool for nonlinear system identificationPeer ReviewedPostprint (published version

Intelligent modelling and active vibration control of flexible manipulator system

Unwanted vibration of flexible manipulator results in unsatisfactory performance of any dynamic system using the flexile manipulator. This paper presents a robust control strategy in order to suppress undesirable vibration due to flexible manipulator maneuver. First, the appropriate model of the flexible manipulator is extracted by applying the control-model identification technique for linear and nonlinear model, namely, autoregressive with exogenous input (ARX) model and nonlinear ARX (NARX) respectively. The linear model is estimated by recursive least square method (RLS) and nonlinear model identified by artificial neural network (NN). Finally, the PID controller is designed for each proposed model to cancel the vibration of the flexible manipulator. The robustness of the controller is evaluated by imposing new disturbances into the linear and nonlinear systems. System identification and controller design is conducted by numerical and simulation approaches. The results from simulation indicate that performance of PID controller using linear model is satisfactory compared to nonlinear model

Neural network-based controllers for an electrothermal furnace system

Neural network schemes are applied in this thesis to a temperature control system problem. The electrothermal furnace is a very popular instrument for applications in material testing area. In this work feedforward neural networks are trained for both identification and control problems of the electrothermal furnace system. The thesis demonstrates that neural networks can be used effectively for this application problem, which is a highly nonlinear dynamical system. The first emphasis is on the electrothermal furnace model identification and the second emphasis is on the design of neural network based PID and internal model control strategies. Both static and dynamic back-propagation methods are discussed. In the electrothermal furnace models that are introduced, multi-layer feedforward networks are interconnected in novel configurations. A novel technique based on the internal model control for nonlinear systems using neural networks is proposed. The control structure proposed directly incorporates a model of the plant that was identified by a neural network and its inverse as part of the control strategy. The potential utilizations of the proposed methods are illustrated through experimental and numerical simulations of an electrothermal furnace system

DNN-Based ADNMPC of an Industrial Pickling Cold-Rolled Titanium Process via Field Enhancement Heat Exchange

The dynamic neural network based adaptive direct nonlinear model predictive control is designed to control an industrial microwave heating pickling cold-rolled titanium process. The identifier of the direct adaptive nonlinear model identification and the controller of the adaptive nonlinear model predictive control are designed based on series-parallel dynamic neural network training by RLS algorithm with variable incremental factor, gain, and forgetting factor. These identifier and controller are used to constitute intelligent controller for adjusting the temperature of microwave heating acid. The correctness of the controller structure, the convergence, and feasibility of the control algorithms is tested by system simulation. For a given point tracking, model mismatch simulation results show that the controller can be implemented on the system to track and overcome the mismatch system model. The control model can be achieved to track on pickling solution concentration and temperature of a given reference and overcome the disturbance

Fuzzy-PID controller on ANFIS, NN-NARX and NN-NAR system identification models for cylinder vortex induced vibration

In this paper, Fuzzy-PID controller on nonlinear system identification models for cylinder due to vortex induced vibration (VIV) has been presented well. Nonlinear system identification models generated after extracting the input-output data from previous paper. The nonlinear model consisted into three methods: Neural Network (NN-NARX) based on the Nonlinear Auto-Regressive with External (Exogenous) Input, Neural Network (NN-NAR) based on the Nonlinear Auto-Regressive and Adaptive Neuro-Fuzzy Inference System (ANFIS). The work has been divided into two main parts: generating the system identification models to predict the system dynamic behavior and using Fuzzy-PID controller to suppress the cylinder vibration arising from the vortices. For system identification models, the best representation for NAR and NARX models has been chosen depend on two variables which are Number of hidden neurons (NE) and number of delay (ND) then using mean Square Error (MSE) to find the best model. Whereas, calculating the lowest MSE when the ND equal to 2 and the value of NE ranging 1-11 then fixing NE which is giving the lowest MSE and calculating it when the ND ranging 1-11. While, for ANFIS model the process consisted of find the lowest MSE at particular number of membership function (MF) with two inputs and generalized bell shape as a type of MF. For the second part, Fuzzy-PID used to attenuate the effect of vortices on the cylinder on the best representation for all methods. However, the consequences presented that the lowest MSE of NAR model equal 2.8452×10-9 when the NE = 6 and ND = 4. While the best model of the NARX method recorded MSE = 1.2714×10-9 at NE and ND equal to 8 and 2 respectively. Also, the lowest MES for ANFIS model recorded 2.5635×10-13 when the MF equal to 2 for input and output. From another hand, Fuzzy-PID controller has been succeeded to reduce the vortex induced vibration on cylinder for all models but particularly on ANFIS model

Nonlinear system identification and control using dynamic multi-time scales neural networks

In this thesis, on-line identification algorithm and adaptive control design are proposed for nonlinear singularly perturbed systems which are represented by dynamic neural network model with multi-time scales. A novel on-line identification law for the Neural Network weights and linear part matrices of the model has been developed to minimize the identification errors. Based on the identification results, an adaptive controller is developed to achieve trajectory tracking. The Lyapunov synthesis method is used to conduct stability analysis for both identification algorithm and control design. To further enhance the stability and performance of the control system, an improved . dynamic neural network model is proposed by replacing all the output signals from the plant with the state variables of the neural network. Accordingly, the updating laws are modified with a dead-zone function to prevent parameter drifting. By combining feedback linearization with one of three classical control methods such as direct compensator, sliding mode controller or energy function compensation scheme, three different adaptive controllers have been proposed for trajectory tracking. New Lyapunov function analysis method is applied for the stability analysis of the improved identification algorithm and three control systems. Extensive simulation results are provided to support the effectiveness of the proposed identification algorithms and control systems for both dynamic NN models

Data-Driven Stability Assessment of Multilayer Long Short-Term Memory Networks

Recurrent Neural Networks (RNNs) are increasingly being used for model identification, forecasting and control. When identifying physical models with unknown mathematical knowledge of the system, Nonlinear AutoRegressive models with eXogenous inputs (NARX) or Nonlinear AutoRegressive Moving-Average models with eXogenous inputs (NARMAX) methods are typically used. In the context of data-driven control, machine learning algorithms are proven to have comparable performances to advanced control techniques, but lack the properties of the traditional stability theory. This paper illustrates a method to prove a posteriori the stability of a generic neural network, showing its application to the state-of-the-art RNN architecture. The presented method relies on identifying the poles associated with the network designed starting from the input/output data. Providing a framework to guarantee the stability of any neural network architecture combined with the generalisability properties and applicability to different fields can significantly broaden their use in dynamic systems modelling and control