B-spline neural networks based PID controller for Hammerstein systems

A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multi-step ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches

Lorenz-like systems and classical dynamical equations with memory forcing: a new point of view for singling out the origin of chaos

A novel view for the emergence of chaos in Lorenz-like systems is presented. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two-well potential, with a forcing term depending on the ``memory'' of the particle past motion. The dynamics of the original Lorenz system in the new particle phase space can then be rewritten in terms of an one-dimensional first-exit-time problem. The emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall. The whole problem is tackled analytically deriving a piecewise linearized Lorenz-like system which preserves all the essential properties of the original model.Comment: 48 pages, 25 figure

generalized predictive control

In this study, the previously proposed Online Support Vector Machines Based Generalized Predictive Control method [1] is applied to the problem of stabilizing discrete-time chaotic systems with small parameter perturbations. The method combines the Accurate Online Support Vector Regression (AOSVR) algorithm [2] with the Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) approach [3] and thus provides a powerful scheme for controlling chaotic maps in an adaptive manner. The simulation results on chaotic maps have revealed that Online SVM-Based GPC provides an excellent online stabilization performance and maintains it when some measurement noise is added to output of the underlying map.C1 Pamukkale Univ, Dept Elect & Elect Engn, TR-20040 Denizli, Turkey

using least squares support vector machines

This work presents a methodology for dynamic reconstruction of chaotic systems from inter-spike interval (ISI) time series obtained via integrate-and-fire (IF) models. In this methodology, least squares support vector machines (LSSVMs) have been employed for approximating the dynamic behaviors of the systems under investigation. Higher generalization capability and avoidance of local minima constitute the main reasons behind the choice of LSSVMs as the approximation toolu. Simulation results have shown that established LSSVM models possess great potential for the reconstruction of chaotic dynamics; in other words, they are able to estimate some dynamic invariants of the underlying chaotic systems as well as they can accurately predict short-term evolution within the horizon of predictability. Moreover, LSSVM models maintain their reconstruction performance even in the case of the existence of noisy data. (c) 2006 Elsevier B.V. All rights reserved.C1 Pamukkale Univ, Dept Elect & Elect Engn, TR-20040 Denizli, Turkey

Support vector machines based neuro-fuzzy control of nonlinear systems

In this work, a novel neuro-fuzzy control structure has been proposed for unknown nonlinear plants, which is referred to as the SVM-based ANFIS controller since it has been emerged from the fusion of adaptive network fuzzy inference system (ANFIS) and support vector machines (SVMs). In the proposed controller, an obtained SVM model of the plant is used to extract the gradient information and to predict the future behavior of the plant dynamics, which are necessary to find the additive correction term and to update the ANFIS parameters. The motivation behind the use of SVMs for modeling the plant dynamics is the fact that the SVM algorithms possess higher generalization ability and guarantee the global minima. The simulation results have revealed that the SVM-based ANFIS controller exhibits considerably high performance by yielding very small transient- and steady-state tracking errors and that it can maintain its performance under noisy conditions. (C) 2010 Elsevier B.V. All rights reserved

control of non-linear systems

In this work, an online support vector machines (SVM) training method (Neural Comput. 2003; 15: 2683-2703), referred to as the accurate online support vector regression (AOSVR) algorithm, is embedded in the previously proposed support vector machines-based generalized predictive control (SVM-Based GPC) architecture (Support vector machines based generalized predictive control, under review), thereby obtaining a powerful scheme for controlling non-linear systems adaptively. Starting with an initially empty SVM model of the unknown plant, the proposed online SVM-based GPC method performs the modelling and control tasks simultaneously. At each iteration, if the SVM model is not accurate enough to represent the plant dynamics at the current operating point, it is updated with the training data formed by persistently exciting random input signal applied to the plant, otherwise, if the model is accepted as accurate, a generalized predictive control signal based on the obtained SVM model is applied to the plant. After a short transient time, the model can satisfactorily reflect the behaviour of the plant in the whole phase space or operation region. The incremental algorithm of AOSVR enables the SVM model to learn the new training data pair, while the decremental algorithm allows the SVM model to forget the oldest training point. Thus, the SVM model can adapt the changes in the plant and also in the operating conditions. The simulation results on non-linear systems have revealed that the proposed method provides an excellent control quality. Furthermore, it maintains its performance when a measurement noise is added to the output of the underlying system. Copyright (c) 2006 John Wiley & Sons, Ltd

three-tank system

This paper presents a support vector machine (SVM) approach to generalized predictive control (GPC) of multiple-input multiple-output (MIMO) nonlinear systems. The possession of higher generalization potential and at the same time avoidance of getting stuck into the local minima have motivated us to employ SVM algorithms for modeling MIMO systems. Based on the SVM model, detailed and compact formulations for calculating predictions and gradient information, which are used in the computation of the optimal control action, are given in the paper. The proposed MIMO SVM-based GPC method has been verified on an experimental three-tank liquid level control system. Experimental results have shown that the proposed method can handle the control task successfully for different reference trajectories. Moreover, a detailed discussion on data gathering, model selection and effects of the control parameters have been given in this paper. (C) 2010 ISA. Published by Elsevier Ltd. All rights reserved

Machines

In this study, the previously proposed Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) method [1] has been applied in controlling the experimental three-tank system. The SVM regression algorithms have been successfully employed in modeling nonlinear systems due to their advantageous peculiarities such as assurance of the global minima and higher generalization capability. Thus, the fact that better modeling accuracy yields better control performance has motivated us to use an SVM model in the GPC loop [1]. In the method, the SVM model of the unknown plant is used to predict future behavior of the plant and also to extract the gradient information which is used in the Cost Function Minimization (CFM) block. The experimental results have revealed that SVM-Based GPC provides very high performance in controlling the system, i.e., the liquid level of the system can track the different types of reference inputs with very small transient- and steady-state errors even in a noisy environment when it is controlled by SVM-Based GPC

Support vector machines-based generalized predictive control

In this study, we propose a novel control methodology that introduces the use of support vector machines (SVMs) in the generalized predictive control (GPC) scheme. The SVM regression algorithms have extensively been used for modelling nonlinear systems due to their assurance of global solution, which is achieved by transforming the regression problem into a convex optimization problem in dual space, and also their higher generalization potential. These key features of the SVM structures lead us to the idea of employing a SVM model of an unknown plant within the GPC context. In particular, the SVM model can be employed to obtain gradient information and also it can predict future trajectory of the plant output, which are needed in the cost function minimization block. Simulations have confirmed that proposed SVM-based GPC scheme can provide a noticeably high control performance, in other words, an unknown nonlinear plant controlled by SVM-based GPC can accurately track the reference inputs with different shapes. Moreover, the proposed SVM-based GPC scheme maintains its control performance under noisy conditions. Copyright (c) 2006 John Wiley & Sons, Ltd.C1 Pamukkale Univ, Dept Elect & Elect Engn, TR-20040 Denizli, Turkey