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In this paper, a novel fuzzy emulated symbolic regression (FESR) model is proposed for modelling and control of Markov jump systems with unknown transition rates. Conventional symbolic regression model is improved in multi-layered form where internal functions, operations and sparse connections are determined via random-learning strategy. A clustering based fuzzy system is designed as a preprocessing-layer that brings an additional power to the model capability. Proposed model includes small number of the output parameters so it is parametrically parsimonious, implementable and easy designed model for future embedded-design applications. In numerical applications first, open-loop black-box modelling results of nonlinear Markov jump systems are shown to discuss the model accuracies where the systems are excited by multi-frequency sine inputs. Modelling results are compared in terms of mean squared-error (MSE) and minimum-descriptive length (MDL) criteria. Second, generalized predictive controller is designed to control the Markov jump systems with proposed model and unknown transition rate where stabilization results are discussed for future applications.

Payload estimators have many parameters, which are trained using the recorded position, velocity and known payload information. To use these payload estimators in the real-time applications, accurate position and velocity information of the system are required. In this paper, first recently proposed sliding-mode observers (SMOs) are designed and compared for velocity estimation of a nonlinear servo system. Second, a parameter estimation based on sliding-mode super-twisting approach is designed to estimate unknown and varying parameter for a class of nonlinear systems. The convergence property of observers is considered using Lyapunov stability method. In the applications, the constant and varying payloads of the servo system have been estimated using the designed method and compared with Extended-Kalman Filter (EKF). In the final section, artificial noises with different SNR are applied to the measurement signal. When the less amplitude of noise signal is applied, second order SMO estimated the states and the payload better than EKF. However, EKF provides much better estimation results than second order SMO for large amplitude of noise signals. For the sake of generalization, second order SMO is a fast and robust observer for small noise cases. In addition, the filtering property of EKF has still importance for large noise cases.

A domestic cookie baking process was modeled using nonlinear forward and inverse models to predict surface temperature, moisture content and browning index that describe the baking quality of the end product. The baking processes were carried out at different oven temperatures (160, 180, 200 °C) and the changes in surface temperature, moisture content and browning index were determined to construct the identification models namely nonlinear polynomial models (PLN) and nonlinear artificial-neural network (ANN) model. The parameters of the artificial models were optimized using least-squares estimation and Levenberg-Marquardt optimization, respectively. The predicted baking characteristics in both forward and inverse phases were in good agreement with the measured ones even for the browning index which was difficult to model because of the its nonminimum-phase dynamics. The application results indicated that the developed intelligient models were very accurate, having low root mean-squared errors, the ANN model approximated the desired values better than the PLN models for all the state variables. Thus, the designed ANN models are applicable for the automatized industrial and domestic oven designs of the future.

In this paper, an adaptive model predictive controller (MPC) with a function approximator is proposed to the control of the uncertain nonlinear systems. The proposed adaptive Sigmoid and Chebyshev neural networks-based MPCs (ANN-MPC and ACN-MPC) compensate the system uncertainty and control the system accurately. Using Lyapunov theory, the closed-loop signals of the linearized dynamics and the uncertainty modeling-based model predictive controller have been proved to be bounded. Accuracy of the ANN-MPC and ACN-MPC has been compared with the Runge–Kutta discretization-based nonlinear MPC on an experimental MIMO three-tank liquid-level system where a functional uncertainty is created on its dynamics. Real-time experimental results demonstrate the effectiveness of the proposed controllers. In addition, due to the faster function approximation capability of Chebyshev polynomial networks, ACN-MPC provided better control performance results. © 2017, The Natural Computing Applications Forum.

In this paper, conventional gradient-descent-based adaptive fuzzy observer is improved by using the terminal sliding-mode theory for a class of nonlinear systems. The improvement is made in two ways: first, the switching term of the sliding-mode approach is added to the state of the observer. Second, the measurement error of the system is designed as the input of the observer instead of measured state. The stability of the observer and boundedness of the parameters are proved using Lyapunov approach. Contributions of the paper are summarized as follows: (i) the robustness and convergence properties of newly proposed observer are improved, (ii) the proposed adaptive fuzzy terminal sliding-mode observer, conventional adaptive fuzzy observer, adaptive neural-network observer, and Euler filtering approaches are compared in terms of their ability to estimate velocities of three real-time experimental systems reliably. The performance of the designed observers is discussed with root mean squared-error criterion where the proposed adaptive fuzzy terminal sliding-mode observer provided much accurate state estimation results than classical observers. © 2015, Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg.

This paper proposes a novel state space least squares support vector machine (SS LS-SVM) for polynomial nonlinear state space (PNLSS) model based recursive system identification. SS LS-SVM, which also possesses an adaptive kernel function, provides an optimum formulation of the monomials (ζ) of the states and input in the PNLSS model. Hence, the PNLSS model encompasses the proposed SS LS-SVM. Recursive nonlinear state space identification is developed in the output error prediction context. The input-output observations are processed sequentially, hence leading to recursive update of the parameters using conventional Gauss-Newton optimization. System states do not need to be measured. However, to to yield a conformal representation of the actual system, number of states need to be known via some physical insight. This characterizes the identification procedure as a grey box one. The PNLSS model is employed in the generalized predictive control (GPC) of a nonlinear continuously stirred tank reactor (CSTR) system. The case which includes additive white noise on the output measurements and a time-varying parameter in the nonlinear system is considered. Numerical applications give the results of a high closed loop identification performance addition to the smooth control input and closely tracking the reference in the GPC scheme. © 2018 IEEE.

The function approximation capability of a regressor model in generalized predictive control (GPC) directly affects the tracking performance of unknown nonlinear systems. In this paper, a novel deep recurrent support vector regressor (DRSVR) is proposed as a function approximator to be adopted in the GPC scheme. This study is an extension of the authors' work [1] to the control task. The DRSVR model has a recurrent state-space structure based on the least-squares support vector regressor (LS-SVR), infinite-impulse response filter (IIR) and adaptive kernel function. The model parameters, including the Gaussian kernel width parameter σ, are updated simultaneously, providing the model to capture the time-varying system dynamics quickly. Parameters are tuned online using error-square minimization via conventional Gauss-Newton optimization while keeping the poles of the IIR filter constrained in the unit circle to maintain stability. The proposed DRSVR based GPC is applied to control nonlinear HIV dynamics. The numerical applications indicate that the proposed regressor model provides high closed loop identification performance in the GPC scheme. Hence, it provides the controller with a significant tracking capability. © 2018 IEEE.

In this article, nonlinear regressor models namely polynomial regressor, artificial neural-network (ANN) and least-squares support vector machine (LS-SVM) were designed and applied to model the drying kinetics and change of the antioxidant properties of mahaleb puree during infrared drying process. Temperature and time were used as the model inputs and moisture ratio, antioxidant capacity and total anthocyanin content were the outputs of nonlinear regressors. The regressor models were compared in terms of the root mean-squared-error (RMSE) and minimum-descriptive-length (MDL) criteria. According to statistical selection criteria, LS-SVM was the best model to describe the infrared drying kinetics of mahaleb puree with the lowest RMSE and MDL values. ANN with Levenberg-Marquardth optimization gave the best results to predict antioxidant capacity and total anthocyanin content during infrared drying process of mahaleb puree. Practical applications: (a) Design and analysis of intelligent models for modeling of drying processes. (b) Design of automatic drying equipments by embedding intelligent models. (c) Prediction of moisture ratio, antioxidant capacity and total anthocyanin of drying mahaleb puree at any time and temperature. © 2018 Wiley Periodicals, Inc.

In this paper, a discretization-based sliding mode observer (DBSMO) is proposed for the state and parameter estimation of nonlinear systems. In the DBSMO structure, an accurate discretized dynamics are derived for the state and parameter update of the sliding mode observer (SMO) instead of integration-based state update. In this way, faster converging observer dynamics are obtained. The stability properties of the conventional SMO remain the same for DBSMO. In the application presented here, first a real-time DC/DC power converter is designed with a computer interface. Then, to show the enhancement of convergence properties, conventional SMO and DBSMO-based model predictive controllers are designed and applied to control of the DC/DC power converter. Through simulation and experimental results, it is shown that the estimation performance of SMO is greatly improved so that the tracking performance is also increased, which are the main contributions of the paper. © 2018, © The Author(s) 2018.

This paper proposes a novel nonlinear gradient-based observer for synchronization and observer-based control of chaotic systems. The model is based on a Runge-Kutta model of the chaotic system where the evolution of the states or parameters is derived based on the error-square minimization. The stability and convergence conditions of observer and control methods are analyzed using a Lyapunov stability approach. In numerical simulations, the proposed observer and well-known sliding-mode observer are compared for the synchronization of a Lü chaotic system and observer-based stabilization of a Chen chaotic system. The noisy case for synchronization and parameter uncertainty case for stabilization are also considered for both observer-based methods. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Soft sensing technology has still important industrial applications especially for chemical reactors, robotic applications, etc. Therefore, this paper introduces and applies novel Runge-Kutta (RK) discretization-based nonlinear observers for real-time sensing applications of unmeasurable quantities. The contribution of the paper is twofold. First, for reliability and accuracy, the stability of the RK based observers are proven. Second, they have been compared with well-known extended-Luenberger observer, extended-Kalman filter and sliding-mode observer on an experimental system. Experiments have shown that the RK model-based observers have a considerable place among conventional ones with respect to design issues and estimation performance for future soft sensing applications. © 2016 TSI® Press.

Artificial Bee Colony (ABC) and Levenberg-Marquardt (LM) optimization algorithms are applied efficiently for nonlinear constrained and unconstrained optimization problems in literature. In this paper, an intelligent hybridization method of the ABC and LM algorithms is proposed such that their global and local exploitation superiorities are unified to reduce the computational time and escape from local minima of optimization problem. In order to prove the capability of proposed hybrid algorithm, twofold experiment is conducted. In the first phase, the hybrid algorithm is applied to optimize several nonlinear unimodal, multimodal and shifted benchmark functions. Secondly, it is applied to the constrained engineering problems and compared to literature works in several performance criteria. © 2017 Elsevier Inc. All rights reserved.

The aim of the online nonlinear system identification is the accurate modeling of the current local input-output behavior of the plant without using any prior knowledge and offline modeling phase. It is a challenging task for many intelligent systems when used for real-time control applications. In this paper, we propose a novel computationally efficient extended fuzzy functions (EFF) model for system identification of unknown nonlinear discrete-time systems. The main contributions are to introduce an effective quasi-nonlinear model (EFF) and propose adaptive learning rates (ALR) for recursive least squares (RLS) and gradient-descent (GD) methods. The asymptotic convergence of the modeling errors and boundedness of the parameters are proved by using the input-to-state stability (ISS) approach. Numerical simulations are performed for Box–Jenkins gas furnace system and a nonlinear dynamic system. The benefits of its accuracy, stability and simple implementation in practice indicate that EFF model is a promising technique for online identification of nonlinear systems. Copyright © 2010 John Wiley & Sons, Ltd.

In this paper, the well-known heuristic Artificial Bee Colony algorithm (ABC) and deterministic Levenberg-Marquardt (LM) optimization method are unified to get better performance of nonlinear optimization. In the proposed cascaded ABC-LM algorithm, the power of the ABC and LM algorithms are synergized to reduce computational-time and get rid of the problem 'stucking at local minima' of some nonlinear functions. Then, the proved power of the cascaded optimization is also tested on the training of Artificial Neural Network (ANN) for classification of XOR data and nonlinear system identification of real-time inverted pendulum set-up. The comparisons in function optimization and system identification using ABC, LM and ABC-LM showed that ABC-LM optimized nonlinear functions and ABC-LM trained ANN has resulted smaller cost functions and mean-squared-error (MSE) values, respectively. © 2013 IEEE.

In this paper, Autoregressive with exogenous input (ARX) and dynamic neural network (DNN) based generalized predictive control (GPC) methods are designed to control of nonlinear systems. ARX and DNN models adaptively approximate the plant dynamics and predict the future behavior of the nonlinear system. While control process goes on, the poles of the ARX and DNN models are constrained in a stable region using a projection operator for structural stability. Simulation results are given to compare the tracking performances of the methods. ARX-GPC and DNN-GPC both yield good tracking performances while keeping the changes in control signal as low as possible. The simulation results show that even though ARX is a linear model, it provides acceptable tracking results as well as DNN model.

In this paper, an adaptive dynamic neural-network observer is designed for unknown or uncertain nonlinear systems and utilized to estimate unmeasurable states. The contributions of paper are in twofold. First, using variable learning rate and internally stable neurons, convergence of parameters is guaranteed and overall stable adaptive observer is designed. Second, designed observer is applied to a real-time flexible-link transmission system data with unmodeled dynamics where the velocities could not be estimated using approximate mathematical model. The SPR condition of the adaptive observer has been satisfied via output error filtering. The boundedness of the estimation error and other signals has been shown using Lyapunov stability. The application results are presented to demonstrate the applicability and efficacy of the designed observer. © 2012 IEEE.

This paper presents a new orthogonal neural network (ONN) which is utilized successively for online identification and control of nonlinear discrete-time systems. The proposed network is designed with auto regressive with exogenous (ARX) terms of inputs and outputs, and their orthogonal terms by Chebyshev polynomials. The network is a single layer neural network and computationally efficient with less number of parameters. The identification by the network is performed in stable sense by using Lyapunov stability guaranteed learning rate. Hence, the learning rate depends on the current knowledge of the system instead of using constant learning rate. This learning rate provides fine online optimization. In simulation study, one benchmark nonlinear system is identified and results are compared. Then, one nonlinear functioned system is identified and controlled by model reference control. From results, it is seen that the proposed model has good learning capability for identification and control.

In this paper, a novel radial basis function (RBF) neural network is proposed and applied successively for online stable identification and control of nonlinear discrete-time systems. The proposed RBF network is a one hidden layer neural network (NN) with its all parameters being adaptable. The RBF network parameters are optimized by gradient descent method with stable learning rate whose stable convergence behavior is proved by Lyapunov stability approach. The parameter update is succeeded by a new strategy adapted from Levenberg-Marquardth (LM) method. The aim of construction of the proposed RBF network is to combine power of the networks which have different mapping abilities. These networks are auto-regressive exogenous input model, nonlinear static NN model and nonlinear dynamic NN model. To apply the model to control of the nonlinear systems, a known sliding mode control is applied to generate input of the system. From simulations; it is sown that the proposed network is an alternative model for identification and control of nonlinear systems with accurate results.

In this paper, a novel radial basis function (RBF) neural network is proposed and applied successively for online stable identification and control of nonlinear discrete-time systems. The proposed RBF network has one hidden layer neural network (NN) with its all parameters being adaptable. The RBF network parameters are optimized by gradient descent method with stable learning rate whose stable convergence behavior is proved by Lyapunov stability approach. The aim of construction of the proposed RBF network is to combine power of the networks which have different mapping abilities. These networks are auto-regressive exogenous input model, nonlinear static NN model and nonlinear dynamic NN model. In simulations, the proposed network is applied for the direct inverse control of one benchmark nonlinear functioned system and Van de Vusse reaction in a CSTR discrete system even there exist large disturbances. From simulations, it is seen that the RBF network with stable learning rate identifies and controls nonlinear systems accurately.