Identification of linear non-stationary dynamical systems

On-Line Eigenvector Algorithms for the Identification of Dynamic Systems

This paper describes the development of a self-feedback Sigma-Pi-linked (/spl Sigma/-/spl Pi/) backpropagation neural network and its applications to dynamical system identification. A self-feedback path is added to each neuron to generate the recursive effect. Each neuron output is recursively related by current input and its preceding output. The introduction of this self-feedback path enables the network to exhibit a dynamic characteristic. Using this complex /spl Sigma/-/spl Pi/-linked architecture, the developed network is capable of performing a system identification for a highly non-linear plant. In the last section of this paper, the function approximation property of this modified network is applied to system identification for different linear and non-linear dynamical systems. This paper also compares the modified network with the conventional backpropagation neural network. Simulation results show that the function approximation property of the modified network is encouraging and can be successfully applied to nonlinear dynamical system identification. >

The network oriented representation of the 3-D electromagnetic structures is based on two types of linear systems. The former one is a dynamic linear system which describes the interaction of electric and magnetic fields inside the structure while the latter one is a linear system consisting of delay lines meant for the reflection and propagation. The system identification of the linear dynamic system needs the estimation of the poles positions and the maximum duration of the delays of complementary linear system. The improved system identification scheme based on poles set stability criterion is introduced. This scheme offers to divide the restored impulse response into the finite duration entire part and the infinite pole part which pertain to the each linear system correspondingly. The simulation results of the model parameter estimation for the two-port coplanar resonator are demonstrated.

Max-plus linear inverse problems: 2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise

This article presents a theoretical framework for the identification of nonlinear dynamic MISO systems with orthonormal base function models on fundamental basics of the Volterra theory. In the past the Volterra theory was used for the identification of nonlinear dynamic SISO systems (e.g. Hammerstein and Wiener models). In principle it is possible to extend these approaches to systems with more than one input (i.e. MISO systems). In former times this failed due to a lack of computational performance. In this paper an approach is presented which allows the identification of arbitrary coupled Hammerstein and Wiener models with multiple inputs. Some fundamental considerations for the identification of MISO systems based on arbitrary coupled Hammerstein models are made and extended to MISO systems based on arbitrary coupled Wiener models. This extended Volterra theory results in equations where the unknown parameters can be separated of the input values in a linear manner. In order to approximate the truncated impulse responses of the linear dynamic systems and to reduce the number of unknown parameters orthonormal base functions (OBFs) are introduced. As an example the proposed identification method is applied to a MISO system based on forward and backward coupled Hammerstein and Wiener models.

The problem of recursive robust identification of linear discrete-time single-input single-output dynamic systems with correlated disturbances is considered. Problems related to the construction of optimal robust stochastic approximation algorithms in the min-max sense are demonstrated. Since the optimal solution cannot be achieved in practice, several robustified stochastic approximation algorithms are derived on the basis of a suitable non-linear transformation of normalized residuals, as well as step-by-step optimization with respect to the weighting matrix of the algorithm. The convergence of the developed algorithms is established theoretically using the ordinary differential equation approach. Monte Carlo simulation results are presented for the quantitative performance evaluation of the proposed algorithms. The results indicate the most suitable algorithms for applications in engineering practice.

The identification of linear dynamic systems in the delta domain has been proposed in this paper with the help of a hybrid metaheuristic algorithm combining chaotic firefly algorithm (CFA) and grey wolf optimiser (GWO). GWO performs the global search, while CFA fine-tunes the solutions through its local search abilities, thereby balancing exploration and exploitation features. Linear systems with static nonlinearities at the input are termed as the Hammerstein model, whereas linear systems with static nonlinearities at the output are known as the Wiener model. A test case with continuous polynomial nonlinearities has been taken up for Hammerstein and Wiener system identification in the delta domain. Delta operator parameterisation unifies identification of continuous-time systems with the discrete domain at a higher sampling rate. Pseudo-random binary sequence (PRBS), polluted with white Gaussian noise of fixed signal-to-noise ratio (SNR), has been considered as the input signal to estimate the unknown model parameters as well as static nonlinear coefficients. The hybrid algorithm not only supersedes the parent heuristics of which it is constituted but also proves better in comparison with some standard and latest heuristic approaches reported in the literature. Nonparametric statistical tests are performed to validate the results. The plots of fitness function (normalised value) against the number of iterations also support the convergence speed and accuracy of the results.

Support vector machines (SVM) are used for system identification of both linear and nonlinear dynamic systems. Discrete time linear models are used to illustrate parameter estimation and nonlinear models demonstrate model structure identification. The VC-dimension of a trained SVM indicates the model accuracy without using separate validation data. We conclude that SVM have potential in the field of dynamic system identification, but that there are a number of significant issues to be addressed.

The linear dynamic systems theory appears to be the most developed part of the control theory. Comparative simplicity of this theory due to the superposition principle dominating there, makes it widely accessible when developing control systems for different kind of processes. Monographs [1, 2, 3] are devoted to numerous analysis and synthesis problems concerning these systems. In the following an approach is developed to linear dynamic plants control algorithms aimed at the estimation of the plant reverse operator for the case when the order of the equation describing the process is unknown.

The generalized Shiryayev sequential probability ratio test (SSPRT) is applied to linear dynamic systems for singlefault isolation and estimation. The algorithm turns out to be the multiple model (MM) algorithm considering all thepossible model trajectories. In real application, this algorithm must be approximated due to its increasing computationcomplexity and the unknown parameters of the fault severeness. The Gaussian mixture reduction is employed toaddress the problem of computation complexity. The unknown parameters are estimated in real time by modelaugmentation based on maximum likelihood estimation (MLE) or expectation. Hence, the system state estimation,fault identification and estimation can be fulfilled simultaneously by a multiple model algorithm incorporating these twotechniques. The performance of the proposed algorithm is demonstrated by Monte Carlo simulation. Although ouralgorithm is developed under the assumption of single fault, it can be generalized to deal with the case of (infrequent)sequential multiple faults. The case of simultaneous faults is more complicated and will be considered in future work.

This paper addresses the parameter estimation problem of an interval-based hybrid dynamical system (interval system). The interval system has a two-layer architecture that comprises a finite state automaton and multiple linear dynamical systems. The automaton controls the activation timing of the dynamical systems based on a stochastic transition model between intervals. Thus, the interval system can generate and analyze complex multivariate sequences that consist of temporal regimes of dynamic primitives. Although the interval system is a powerful model to represent human behaviors such as gestures and facial expressions, the learning process has a paradoxical nature: temporal segmentation of primitives and identification of constituent dynamical systems need to be solved simultaneously. To overcome this problem, we propose a multiphase parameter estimation method that consists of a bottom-up clustering phase of linear dynamical systems and a refinement phase of all the system parameters. Experimental results show the method can organize hidden dynamical systems behind the training data and refine the system parameters successfully.

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author’s work, concerning parameter identification of linear dynamic stochastic system. Special attention is given to searching the solution of an equation in a neighbourhood of some initial approximation.

A linear dynamic system is considered. Orthogonal series procedures are developed to recover the state and its derivative. The uniform mean square error convergence is investigated. An application to identification and open-loop control is discussed.

IDENTIFICATION AND MINIMAL REALIZATION OF MULTIVARIABLE SYSTEMS

The paper demonstrates that radial basis function network (RBFN) with adaptive centers and width can be used effectively for identification of nonlinear dynamic system. The proposed RBFN is trained by hybrid learning algorithm, which uses conjugate gradient optimization algorithm to obtain the center and width of each radial basis function and the least squares method to obtain the weights. To avoid capturing a local optimum, regularization error energy function is used and the centers of basis functions are initialized using a fuzzy C-means clustering method. Simulation results reveal that the identification schemes based on RBFN gives considerably better performance and show faster learning in comparison to previous methods