Blind parametric identification of non-Gaussian FIR systems using higher order cumulants

Two approaches are introduced for the identification of linear time-invariant systems when only output data are available. The input sequences are independent and must be non-Gaussian. To estimate the parameters of the system, we use only the fourth-order cumulants of the output, which may be contaminated by an additive, zero mean, Gaussian noise of unknown variance. To measure the performance of the proposed algorithms against existing methods, we compared them with the Zhang's algorithm. Simulations verify an apparent performance of the second algorithm, compared with the first and Zhang's algorithms, in a low signal-to-noise ratio and for small data. The simulation results show that the first algorithm has the same performance compared with Zhang's one. But the second algorithm achieves better performance compared with the first and Zhang is algorithm. For validation purposes, the second algorithm is used to search for a model able to describe and simulate the data set representing the wind speed.     

Identification of linear systems using input-output cumulants

A new identification method is proposed for estimating the parameters of a discrete-time linear dynamic system excited by non-gaussian inputs using kth order (k > 2) cumulants of input and output signals contaminated by additive (possibly coloured) gaussian noise. The parameter estimates obtained by this method are proved to be consistent under weak conditions. This method has an on-line algorithm for computing the parameter estimates, just like the least-squares method. A simulation example is included to demonstrate the effectiveness of this method.     

Identification of a two-link flexible manipulator using adaptivetime delay neural networks

This paper deals with identification of a two-link flexible manipulator belonging to a class of multi-input, multi-output (MIMO) nonlinear systems, by using adaptive time delay neural networks (ATDNNs). Two neuro-dynamic identifiers are proposed. The capabilities of the proposed structures for representing the nonlinear input-output map of the flexible manipulator are shown analytically. Selection criteria for specifying the fixed structural parameters as well as the adaptation laws for updating the adjustable parameters of the networks are provided. During identification, the two-link flexible manipulator is under nonlinear control and the input-output data sets are generated for different desired trajectories. Simulation results reveal that the proposed neuro-dynamic structures are capable of successfully identifying a highly nonlinear system without any a priori information about the nonlinearities of the system and without any off-line training.     

Identification of nonlinear dynamical systems using multilayered neural networks

A novel multilayer discrete-time neural net paradigm is presented for the identification of multi-input multi-output (MIMO) nonlinear dynamical systems. The major novelty of this approach is a rigorous proof of identification error convergence that reveals a requirement for a new identifier structure and nonstandard weight tuning algorithms. The NN identifier includes modified delta rule weight tuning and exhibits a learning-while-functioning feature instead of learning-then-functioning, so that the identification is on-line with no explicit off-line learning phase needed. The structure of the neural net (NN) identifier is derived using a passivity aproach. Linearity in the parameters is not required and certainty equivalence is not used. The notion of persistency of excitation (PE) and passivity properties of the multilayer NN are defined and used in the convergence analysis of both the identification error and the weight estimates.     

Well reservoir model identification using translation and scale invariant higher order networks

This paper describes the use of higher order neural networks to identify well reservoir response models from test data. Well reservoir response models are characterised by a family of parametrically related curves. Neural networks can in principle offer an interesting approach to the identification problem as data are often uncertain and incomplete. However, it turns out that the well reservoir model, viewed as a curve in two dimensions, is invariant with respect to translation and changes of scale of the axes. This poses severe problems for a standard backpropagation network using the two-dimensional plot as an input retina. This difficulty can be overcome by using a higher order network in which the output is forced to be invariant with respect to the required transformations of the retina. In this way, the potentially huge number of weights is significantly reduced using the invariance condition as a constraint which acts so as to divide the weights into equivalence classes within which they are equal. The resulting network can then be trained using standard techniques. We contrast this network approach with classical methods of model identification.     

Identification of linear and nonlinear dynamic systems using recurrent neural networks

This paper describes the use of Elman-type recurrent neural networks to identify dynamic systems. Networks as originally designed by Elman (Cognitive Sci., 1990, 14, 179–211) and also those in which self-connections are made to the context units were employed to identify a variety of linear and nonlinear systems. It was found that the latter networks were more versatile than the basic Elman nets in being able to model the dynamic behaviour of high order linear and nonlinear systems.     

Identification of nonlinear dynamic systems using functional linkartificial neural networks

We have presented an alternate ANN structure called functional link ANN (FLANN) for nonlinear dynamic system identification using the popular backpropagation algorithm. In contrast to a feedforward ANN structure, i.e., a multilayer perceptron (MLP), the FLANN is basically a single layer structure in which nonlinearity is introduced by enhancing the input pattern with nonlinear functional expansion. With proper choice of functional expansion in a FLANN, this network performs as good as and in some cases even better than the MLP structure for the problem of nonlinear system identification.     

On the "Identification and control of dynamical systems using neural networks"

Referring to the above said paper by Narendra-Parthasarathy (ibid., vol.1, p4-27 (1990)), it is noted that the given Example 2 (p.15) has a third equilibrium state corresponding to the point (0.5, 0.5).     

Nonlinear internal model control using neural networks: applicationto processes with delay and design issues

We propose a design procedure of neural internal model control systems for stable processes with delay. We show that the design of such nonadaptive indirect control systems necessitates only the training of the inverse of the model deprived from its delay, and that the presence of the delay thus does not increase the order of the inverse. The controller is then obtained by cascading this inverse with a rallying model which imposes the regulation dynamic behavior and ensures the robustness of the stability. A change in the desired regulation dynamic behavior, or an improvement of the stability, can be obtained by simply tuning the rallying model, without retraining the whole model reference controller. The robustness properties of internal model control systems being obtained when the inverse is perfect, we detail the precautions which must be taken for the training of the inverse so that it is accurate in the whole space visited during operation with the process. In the same spirit, we make an emphasis on neural models affine in the control input, whose perfect inverse is derived without training. The control of simulated processes illustrates the proposed design procedure and the properties of the neural internal model control system for processes without and with delay.     

Identification of linear systems with noisy input using input-output cumulants

An identification method is presented for estimating the parameters of a discrete-time linear dynamic system excited by non-gaussian input signals using the fourth-order cumulants of the input and output signals, both of which are contaminated by additive gaussian noise. Two types of estimators of the fourth-order cumulants of the input and output signals are proposed for this method. The first is conventional. The second, which is new allows us only to have a recursive algorithm for computing the parameter estimators. The parameter estimators obtained by this algorithm are shown to be strongly consistent under certain weak conditions. Simulation examples are included to demonstrate the effectiveness of the proposed method.     

Identification of structural systems by neural networks

A method based on the use of neural networks is developed for the identification of systems encountered in the field of structural dynamics. The methodology is applied to the identification of linear and nonlinear dynamic systems such as the damped Duffing oscillator and the Van der Pol equation. The “generalization” ability of the neural networks is used to predict the response of the identified systems under deterministic and stochastic excitations. It is shown that neural networks provide high fidelity models of unknown structural dynamic systems, which are used in applications such as structural control, health monitoring of structures, earthquake engineering, etc.     

一类基于微分方程模型具有连续分布延迟神经网络的稳定性分析

考虑一类基于微分方程具有连续分布延迟的神经网络模型。利用Lozinskii方法的性质和微分不等式方法,获得了这类具有连续分布延迟的神经网络的渐近稳定的一些充分条件,结果去掉了对激励函数有界性的要求。     

小波和神经网络在心音识别中的应用

提出一种心音的特征提取和分类方法,用离散小波变换分解、重构产生信号的细节包络,进而用于提取特征,从预处理的信号中提取统计特性,作为心音分类的特征。多层感知器用于心音的分类,并通过250个心动周期得到验证,算法识别率达到92%。     

Stabilization of unknown nonlinear systems using neural networks

This paper deals with stabilization of unknown nonlinear systems using a nonlinear controller made with a backpropagation neural network. Control strategies based on an inverse state neural model built from an off-line learning step are proposed. The proposed strategies can be implemented following two approaches. The first one consists on computing control horizon based on actual state vector and desired one at a future instant. The second approach applies control action in the sense of a receding horizon. Adaptive control has been considered where the updating of the neural controller is accomplished to optimize different control objectives.     

Stable control of nonlinear systems using neural networks

A neural-network-based direct control architecture is presented that achieves output tracking for a class of continuous-time nonlinear plants, for which the nonlinearities are unknown. The controller employs neural networks to perform approximate input/output plant linearization. The network parameters are adapted according to a stability principle. The architecture is based on a modification of a method previously proposed by the authors, where the modification comprises adding a sliding control term to the controller. This modification serves two purposes: first, as suggested by Sanner and Slotine,¹ sliding control compensates for plant uncertainties outside the state region where the networks are used, thus providing global stability; second, the sliding control compensates for inherent network approximation errors, hence improving tracking performance. A complete stability and tracking error convergence proof is given and the setting of the controller parameters is discussed. It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes. Two simulations are provided to demonstrate the features of the control method.     

Control of perturbed systems using neural networks.

Stability conditions for a perturbed plant control by a conventional robust controller and a neurocontroller are presented. The neural net-based direct inverse controller is proposed to aid the robust controller to further suppress the output error resulting from the unmodeled residuals. A procedure for determining the permissible network's output under which the overall closed-loop system will be robustly stable is provided.     

Nonlinear adaptive control using neural networks and its application to CSTR systems

In this paper, adaptive tracking control is considered for a class of general nonlinear systems using multilayer neural networks (MNNs). Firstly, the existence of an ideal implicit feedback linearization control (IFLC) is established based on implicit function theory. Then, MNNs are introduced to reconstruct this ideal IFLC to approximately realize feedback linearization. The proposed adaptive controller ensures that the system output tracks a given bounded reference signal and the tracking error converges to an -neighborhood of zero with being a small design parameter, while stability of the closed-loop system is guaranteed. The effectiveness of the proposed controller is illustrated through an application to composition control in a continuously stirred tank reactor (CSTR) system.     

Stable adaptive control using fuzzy systems and neural networks

Stable direct and indirect adaptive controllers are presented, which use Takagi-Sugeno fuzzy systems, conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous-time nonlinear plants with poorly understood dynamics. The indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller. We prove that with or without such knowledge both adaptive schemes can “learn” how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of a reference input. In addition, for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation. The performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane     

Control of nonlinear dynamical systems using neural networks:controllability and stabilization

An attempt is made to indicate how practically viable controllers can be designed using neural networks, based on results in nonlinear control theory. The problem of stabilization of a dynamical system around an equilibrium point when the state of the system is accessible is considered. Simulation results are included to complement the theoretical discussions.