Identification of nonlinear systems using new dynamic neural network structures

Multi-scale fuzzy modeling of multivariable discrete-time nonlinear dynamical systems is approached analytically in this paper. The underlying idea of this approach is to introduce the idea of multi-scale fuzzy quantization. More globally supported membership functions are used at coarser scales to capture global characteristics of the unknown system, whereas more locally supported membership functions are used at finer scales to fill in the local features. Starting from the coarsest scale down to finer ones, a projection method is used to extract a partial fuzzy-model (in terms of fuzzy membership functions and fuzzy rules) from the residual of the system at each scale until the residual drops below a prescribed modeling error bound. The multi-scale fuzzy model is then obtained by assembling the partial fuzzy models together. To reach a near optimal fuzzy model, a rule reduction technique has also been developed to delete some fuzzy rules. An illustrative example is used to demonstrate the effectiveness of the scheme.

The paper proposes a new method for identifying orders of input-output models for unknown nonlinear dynamic systems. The approach is based on the continuity property of the nonlinear functions which represent input-output models of continuous dynamic systems. The approach does not depend on any nonlinear function approximation methods and solely depends on the system's input-output data measured in experiments. By evaluating the modification of an index which is defined as Lipschitz number with the successive modification of model orders, the appropriate model orders can be determined simply and reliably. Theoretical background of the present approach is discussed. Several examples from chaotic dynamic systems, nonlinear plant models are presented to demonstrate the effectiveness of the present method.

The paper presents a review of the studies that were conducted at Energy Systems Institute (ESI) SB RAS in the field of mathematical modeling of nonlinear input-output dynamic systems with Volterra polynomials. The first part presents an original approach to identification of the Volterra kernels. The approach is based on setting special multi-parameter families of piecewise constant test input signals. It also includes a description of the respective software; presents illustrative calculations on the example of a reference dynamic system as well as results of computer modeling of real heat exchange processes. The second part of the review is devoted to the Volterra polynomial equations of the first kind. Studies of such equations were pioneered and have been carried out in the past decade by the laboratory of ill-posed problems at ESI SB RAS. A special focus in the paper is made on the importance of the Lambert function for the theory of these equations.

Identification of nonlinear systems by use of nonstationary white-noise inputs

Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot

This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system.

Nonlinear dynamic systems are characterized with uncertainties in terms of structure and parameters. These uncertainties cannot be described by deterministic models. The modelling and identification of nonlinear dynamic systems through the measured experimental data is a problem in engineering and technical processes. Therefore, field of system identification have become an important area of research. Fuzzy technology is an effective tool for dealing with complex nonlinear processes that are characterized with uncertain factors. In this paper, a novel approach based on Local Linear method learning in dynamical filter weights neurons for the identification of non-linear dynamic systems is presented. The fuzzy wavelet neural network combines wavelet theory with fuzzy logic and neural networks. Learning fuzzy rules and parameter update in fuzzy wavelet neural network is based on gradient decent method. The proposed approach is said to be Fuzzy Local Linear Wavelet Neural Network based model. It has been explained through examples. The structure is tested for the identification with both wavelet neural network and Fuzzy Local Linear Wavelet Neural Network that shows the comparative performance.KeywordsSystem IdentificationNon-linear SystemWavelet Neural NetworkFuzzy Wavelet Neural NetworkLocal Linear Wavelet Neural NetworkFuzzy Local Linear Wavelet Neural Network

In this paper, a model of nonlinear dynamic system with Lévy jumps based on cargo sorting DNA robot is studied. Firstly, nonlinear biochemical reaction system based on cargo sorting DNA robot model is established. Considering the influence of external disturbances on the system, nonlinear biochemical reaction system with Lévy jump is built and its dimensionality is reduced. Secondly, in order to prove that the built system conforms to the actual meaning, the existence and uniqueness of the system solution is verified. Next, the sufficient conditions for the completion of cargo pick-up of cargo sorting DNA robot and the continued sufficiency are introduced, and the progress of cargo sorting DNA robot under different noise intensities is analyzed. Then, it is proved that the positive recursion of the reaction can better describe and show the persistence of the system. Finally, numerical simulations verify the correctness of the theoretical results. The results show that the end of cargo pick-up with DNA robots for cargo sorting is closely related to the intensity of noise.KeywordsCargo sorting DNA robotNonlinear system modelLévy jumpLyapunov functionPositive recursion

The problem of creating mathematical models of nonlinear dynamical systems does not have an unambiguous solution and requires the creation of a separate synthesis method for each such object. To develop a method for synthesizing mathematical models of an extensive class of nonlinear dynamical systems with polynomial nonlinearities. The work uses a method based on the solution of the Volterra integral equation in the ideology set forth in Van Trees H.L., according to which the structure of a nonlinear dynamical object present47s a series connection of the linear part, characterizing the inertial properties of the system, and the nonlinear element, given by static characteristic. The difference of the suggested version of the method from the classical one, proposed in the works of Van Trees H.L., is an expansion of their input and output signals into Fourier series and a representation of the inertial part of these systems by their Bode plots, connected into one structure with input and output signals and non-linearity by Volterra integral equation. The algorithm of the proposed method is disclosed by the example of solving the problem of identifying a nonlinear dynamical system which impulse response of the inertial part satisfies the separability requirement, the order of the polynomial nonlinearity is three, and the model of the input signal has the form of a sinusoid "raised" over the time axis on a priori given constant level. A computational experiment was carried out on the example of nonlinear dynamical systems with the third order of the nonlinear characteristic and the first and second orders of the model of the inertial part of these systems with the specified algorithms of their parametric identification. The suggested method allows to synthesis the mathematical model of a nonlinear dynamical system with the polynomial static characteristic to the case when the input signal has an arbitrary number of harmonics, and the model of the inertial part and the nonlinear polynomial function have an arbitrary order.

Fuzzy recurrent stochastic configuration networks (FRSCNs) are a class of randomized neurofuzzy models that have shown success in modeling nonlinear dynamic systems. However, the data generated from the real-world industry process often exhibits nonstationary characteristics, which could lead to the resulting model with poor generalization performance. This article presents an online self-learning FRSCN (OSL-FRSCN) for problem-resolving. OSL-FRSCNs integrate the self-organizing learning strategies into FRSCNs, maintaining the model's strong fuzzy inference capabilities while enhancing their continuous learning abilities for nonstationary data streams. The network parameters are updated online using the projection algorithm based on the newly arriving data streams. Moreover, the network structure can be dynamically adjusted in the light of the fuzzy recurrent stochastic configuration (FRSC) algorithm and an improved sensitivity analysis. Comprehensive comparisons over two nonlinear system identification tasks and two industrial applications are carried out. Numerical results clearly demonstrate that the proposed OSL-FRSCNs outperform other neurofuzzy and nonfuzzy models with sound generalization, verifying their effectiveness in modeling nonlinear systems with nonstationary dynamics.

In this paper we present and compare different fault diagnosis algorithms using space space models for nonlinear dynamic systems. Most fault diagnosis and isolation algorithms for dynamic systems, which can be modeled using a set of state space equations, have relied on the system being linear and the noise and disturbances being Gaussian. In such cases, optimal filtering ideas based on Kalman filtering are utilized in estimation followed by a residual analysis, for which whiteness tests are typically carried out. Linearized approximations (e.g., Extended Kalman filters) have been used in the nonlinear dynamic systems case. However, linearization techniques, being approximate, tend to suffer from poor detection or high false alarm rates. In this paper, we use the sequential Monte Carlo filtering approach where the complete posterior distribution of the estimates are represented through samples or particles as opposed to the mean and covariance of an approximated Gaussian distribution. The particle filter is combined with the innovation-based fault detection techniques to develop a fault detection and isolation scheme. The advantage of particle filters is that they are capable of handling any functional nonlinearity and system or measurement noise of any distribution. An improvement on using a single Extended Kalman filter matched to a particular model is to use the the Interacting Multiple Model estimator, which consists of a number of EKFs running in parallel. Such a multiple model estimator can handle the abrupt changes in the system dynamics, which is essential for fault diagnosis. Here, we compare the fault detection performances of these algorithms on different nonlinear systems.

The efficacy of the multimodel framework (MMF) in modeling and identification of complex, nonlinear, and uncertain systems has been widely recognized in the literature owing to its simplicity, transparency, and mathematical tractability, allowing the use of well-known modeling analysis and control design techniques. The approach proved to be effective in addressing some of the shortcomings of other modeling techniques such as those based on a single nonlinear autoregressive network with exogenous inputs model or neural networks. A great number of researchers have contributed to this active field. Due to the significant amount of contributions and the lack of a recent survey, the review of recent developments in this field is vital. In this two-part paper, we attempt to provide a comprehensive coverage of the multimodel approach for modeling and identification of complex systems. The study contains a classification of different methods, the challenges encountered, as well as recent applications of MMF in various fields. Part 1 of this paper presents an overview of MMF for modeling and identification of nonlinear systems as well as the review of recent developments in the partitioning strategies employed.

NOE TS fuzzy modelling of nonlinear dynamic systems with uncertainties using symbolic interval-valued data

In this paper, the use of radial basis function network (RBFN) for simultaneous online identification and indirect adaptive control of nonlinear dynamical systems is demonstrated. The motivation of using RBFN comes from the simplicity of its structure and simpler mathematical formulation, which gives it an advantage over multi-layer feed-forward neural network (MLFFNN). Since most processes are nonlinear, the use of conventional proportional-integral-derivative controller is not useful. Most of the time plant’s dynamics information is not available. This creates another limitation on the use of conventional control techniques, which works only if plant’s dynamics information is available. The proposed controller is tested for parameter variations and disturbance effects. Simulation results showed that RBFN is able to capture the unknown dynamics as well as simultaneously able to adaptively control the plant. It is also found to compensate the effects of parameter variations and disturbances. The comparative analysis is also done with MLFFNN in each simulation example, and it is found that performance of RBFN is better than that of MLFFNN.

This book presents a systematic framework targeting at fuzzy modeling and fuzzy control of nonlinear systems with uncertainties. The book is organized into three major parts incorporating 13 chapters. The first part contains four chapters focusing on the modeling of nonlinear dynamical systems by using fuzzy logic. The second part includes five chapters in which fuzzy inference and control techniques are addressed. The final part consists of four chapters, which covers several advanced topics in fuzzy control ranging from controller and filter design to chaotification of fuzzy systems and feedforward fuzzy control of nonlinear systems via Fourier integrals. One of the major contributions of this book is that it presents the latest original research developments in the field. It provides rich examples and references, too. It is a valuable resource for those researchers and practitioners interested in expanding their knowledge from fuzzy logic and applications to nonlinear dynamical systems.