Identification Of Discrete-time Systems Research Articles

Frequency-Domain Identification of Discrete-Time Systems using Sum-of-Rational Optimization

This paper proposes a new computationally tractable method to fit coefficients of a fixed-order discrete-time transfer function to a measured frequency response, with stability guaranteed. The problem is formulated as a non-convex global sum-of-rational optimization problem whose objective function is the sum of weighted squared residuals at each observed frequency datapoint. Stability is enforced using a polynomial matrix inequality constraint. The problem is solved by a moment-sum-of-squares hierarchy of semidefinite programs through a framework for sum-of-rational-functions optimization. Convergence of the moment-sum-of-squares program is guaranteed as the bound on the degree of the sum-of-squares polynomials approaches infinity. The performance of the proposed method is demonstrated using numerical simulation examples.

Combined invariant subspace & frequency-domain subspace method for identification of discrete-time MIMO linear systems

Combined invariant subspace & frequency-domain subspace method for identification of discrete-time MIMO linear systems

Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems

The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems. The general idea and conceptual approaches are developed following recent results on machine-learning based identification of the Koopman operator using autoencoders and DMDc for finite-dimensional discrete-time system identification. The resulting linear reduced order model is combined with a classical Kalman Filter for state reconstruction with minimum error covariance as well as a reduced order observer with very low computational and memory demands. The performance of the two schemes is evaluated and compared in terms of the approximated L2 error norm in a numerical simulation study. It turns out, that for the evaluated case study the reduced-order scheme achieves comparable performance with significantly less computational load.

Идентификация в дискретных системах со случайными скачкообразными параметрами при неполной информации

Рассмотрена задача идентификации в дискретной системе со скачкообразными параметрами. Алгоритм предполагает использование оценок, построенных с помощью экстраполятора Калмана с оценками неизвестных входов и оценками неизвестных входов в модели вектора наблюдения. Для иллюстрации предлагаемого подхода приведен пример.

Comparison of Crossover in Genetic Algorithm for Discrete-Time System Identification

System identification is a process where a mathematical model is derived in order to explain dynamical behaviour of a system. One of its step is model structure selection and it is crucial that, in this step, an adequate model i.e. a model with a good balance between parsimony and accuracy of the model is selected in approximating the system. Genetic algorithm (GA), a method known for optimisation, is used for selecting a model structure. GA is known to be able to reduce much computational burden. This paper investigates the effect of different types of crossover, namely, single-point, double-point, multiple-point and uniform crossover, within GA in producing an optimum model structure for system identification. This was carried out using a computational software on a number of simulated data. As a conclusion, using Akaike Information Criterion as objective function, single point crossover produces the model with the best balance in most of the tests.

Stochastic output delay identification of discrete-time Gaussian systems

In this paper we propose a solution to the problems of detecting a generally correlated stochastic output delay sequence of a linear system driven by Gaussian noise. This is the model for uncertain observations resulting from losses in the propagation channel due to fading phenomena or packet dropouts that is common in wireless sensor networks, networked control systems, or remote sensing applications. The solution we propose consists of a nonlinear detector which identifies online the stochastic delay sequence. The solution provided is optimal in the sense that minimizes the probability of error of the delay detector. Finally, a filtering stage fed with the information given by the detector can follow to estimate the state of the system. Numerical simulations show good performance of the proposed method.

Iterative Identification of Discrete-Time Systems With Bilinear Forms in the Presence of Colored Noises Based on the Hierarchical Principle

The paper focuses on the identification of discrete-time bilinear forms in the special case when the external noise (disturbance) is an autoregressive average moving process. The proposed estimation procedure is iterative where, at each iteration, two sets of parameter vectors are estimated interactively. Using the hierarchical technique, a hierarchical generalized extended least squares-based iterative (H-GELSI) algorithm is proposed for avoiding estimating the redundant parameters. In contrast to the hierarchical generalized extended gradient-based iterative (H-GEGI) algorithm, the proposed algorithm can give more accurate parameter estimates. The main results derived in this paper are verified by means of both the computational efficiency comparison and two numerical simulations.

Approximate Nonlinear Regulation via Identification-Based Adaptive Internal Models

This paper concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which become asymptotic whenever a "right" internal model exists in the identifier's model set. The proposed approach, moreover, does not require "high-gain" stabilization actions.

Robust identification of discrete-time linear systems with unknown time-varying disturbance

In this paper, one robust identification method is proposed for the discrete-time linear systems with unknown time-varying disturbance. The disturbance is considered as a time-varying parameter for tracking estimation. A robust recursive least squares method is proposed using a forgetting factor. Moreover a new forgetting scheme to update the covariance matrix is developed to improve the stable convergence property of the time-invariant model parameters and the tracking performance of time-varying disturbance. The convergence performance of parameter estimation is analyzed with a proof. Two examples with different types of time-varying disturbance are shown to illustrate the effectiveness and advantage of the proposed method.

Further Results on Stabilizability of Discrete-time Nonlinearly Parameterized Systems With Scalar Parameters

This note advances the work “ Simultaneous identification and stabilization of nonlinearly parameterized discrete-time systems by nonlinear least squares algorithm ” by Li and Chen by allowing the sensitivity functions of discrete-time nonlinearly parameterized systems with scalar parameters admitting arbitrarily many zeros for large outputs. Stabilizability theorems” and “impossible theorems” have been provided both for time-invariant-parameter and time-varying-parameter cases. A practical estimation algorithm is also proposed to facilitate the implementation in computations.

Discrete-time system identification based on novel information criterion using genetic algorithm

Model structure selection is a problem in system identification which addresses selecting an adequate model i.e. a model that has a good balance between parsimony and accuracy in approximating a dynamic system. Parameter magnitude-based information criterion 2 (PMIC2), as a novel information criterion, is used alongside Akaike information criterion (AIC). Genetic algorithm (GA) as a popular search method, is used for selecting a model structure. The advantage of using GA is in reduction of computational burden. This paper investigates the identification of dynamic system in the form of NARX (Non-linear AutoRegressive with eXogenous input) model based on PMIC2 and AIC using GA. This shall be tested using computational software on a number of simulated systems. As a conclusion, PMIC2 is able to select optimum model structure better than AIC.

Accurate Lithium-ion battery parameter estimation with continuous-time system identification methods

The modeling of Lithium-ion batteries usually utilizes discrete-time system identification methods to estimate parameters of discrete models. However, in real applications, there is a fundamental limitation of the discrete-time methods in dealing with sensitivity when the system is stiff and the storage resolutions are limited. To overcome this problem, this paper adopts direct continuous-time system identification methods to estimate the parameters of equivalent circuit models for Lithium-ion batteries. Compared with discrete-time system identification methods, the continuous-time system identification methods provide more accurate estimates to both fast and slow dynamics in battery systems and are less sensitive to disturbances. A case of a 2nd-order equivalent circuit model is studied which shows that the continuous-time estimates are more robust to high sampling rates, measurement noises and rounding errors. In addition, the estimation by the conventional continuous-time least squares method is further improved in the case of noisy output measurement by introducing the instrumental variable method. Simulation and experiment results validate the analysis and demonstrate the advantages of the continuous-time system identification methods in battery applications.

A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear functional forms and their associated parameters from a limited number of time-series data points. For this, we cast this identification problem as a sparse linear regression problem and take a Bayesian viewpoint to solve it. As such, this approach typically leads to nonconvex optimisations. We propose a convexification procedure relying on an efficient iterative re-weighted $\ell_1$-minimisation algorithm that uses general sparsity inducing priors on the parameters of the system and marginal likelihood maximisation. Using this approach, we also show how convex constraints on the parameters can be easily added to our proposed iterative re-weighted $\ell_1$-minimisation algorithm. In the supplementary material \cite{appendix}, we illustrate the effectiveness of the proposed identification method on two classical systems in biology and physics, namely, a genetic repressilator network and a large scale network of interconnected Kuramoto oscillators.

An Improved Global Harmony Search Algorithm for the Identification of Nonlinear Discrete-Time Systems Based on Volterra Filter Modeling

This paper describes an improved global harmony search (IGHS) algorithm for identifying the nonlinear discrete-time systems based on second-order Volterra model. The IGHS is an improved version of the novel global harmony search (NGHS) algorithm, and it makes two significant improvements on the NGHS. First, the genetic mutation operation is modified by combining normal distribution and Cauchy distribution, which enables the IGHS to fully explore and exploit the solution space. Second, an opposition-based learning (OBL) is introduced and modified to improve the quality of harmony vectors. The IGHS algorithm is implemented on two numerical examples, and they are nonlinear discrete-time rational system and the real heat exchanger, respectively. The results of the IGHS are compared with those of the other three methods, and it has been verified to be more effective than the other three methods on solving the above two problems with different input signals and system memory sizes.

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

Although a vast number of techniques for the identification of nonlinear discrete-time systems have been introduced, the identification of continuous-time nonlinear systems is still extremely difficult. In this paper, the Nonlinear Difference Equation with Moving Average noise (NDEMA) model which is a general representation of nonlinear systems and contains, as special cases, both continuous-time and discrete-time models, is first proposed. Then based on this new representation, a systematic framework for the identification of nonlinear continuous-time models is developed. The new approach can not only detect the model structure and estimate the model parameters, but also work for noisy nonlinear systems. Both simulation and experimental examples are provided to illustrate how the new approach can be applied in practice.

New Approaches to Identification of PWARX Systems

We consider the clustering-based procedures for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. These methods exploit three main techniques which are clustering, linear identification, and pattern recognition. The clustering method based on thek-means algorithm is treated in this paper. It consists in estimating both the parameter vector of each submodel and the coefficients of each partition while knowing the model ordersnaandnband the number of submodelss. The performance of this approach can be threatened by the presence of outliers and poor initializations. To overcome these problems, we propose new techniques for data classification. The proposed techniques exploit Chiu’s clustering technique and the self-artificial Kohonen neural network approach in order to improve the performance of both the clustering and the final linear regression procedure. Simulation results are presented to illustrate the performance of the proposed method.

New results on discrete-time delay systems identification

A new approach for simultaneous online identification of unknown time delay and dynamic parameters of discrete-time delay systems is proposed in this paper. The proposed algorithm involves constructing a new generalized regression vector and defining the time delay and the rational dynamic parameters in the same vector. The gradient algorithm is used to deal with the identification problem. The effectiveness of this method is illustrated through simulation.

Identification of discrete-time bilinear systems through equivalent linear models

This paper presents a novel method for identification of discrete-time, time-invariant state-space models of bilinear dynamical systems using the steady-state portion of a single input/multiple output time-history measurements. These measurements are recorded by exciting the system with a linear combination of sine and cosine functions of user-selected frequencies enriched by a subtle amount of random component. The proposed method relies on conversion of the bilinear system into an equivalent linear model (ELM) by an accurate approximation of the state in the bilinear term using a set of sine and cosine basis functions whose frequencies are obtained as combinations of the input frequencies. Observer/Kalman Filter Identification (OKID), a linear time invariant (LTI) system identification algorithm, is used to identify the aforementioned ELM from which the original bilinear model is recovered. A numerical example is also provided.

On embedded FIR filter models for identifying continuous-time and discrete-time transfer functions: the RPM approach

For identifying a continuous-time (CT) transfer function model, data filtering is a solution which provides the necessary unmeasurable input--output derivative approximations. In discrete-time (DT) system identification, the well-known ARX model can be used successfully if the estimate is performed with suitable prefiltered data. This article describes the reinitialised partial moment (RPM) model which embeds implicitly a finite impulse response filter in both CT and DT domains. With knowledge of the important role of data prefiltering in standard methods, this RPM model embedded filter gives particular properties to this original tool. Although both the CT RPM model and the DT RPM model present an embedded filter, the formulation and the implementation in the CT and the DT domains are different. Therefore, the aim of this article is to present a tutorial on the RPM models and to give an overview of all the applications.

Discrete system identification and self-tuning control of dissolved oxygen concentration in a stirred reactor

This work presents the applications of discrete-time system identification and generalized minimum variance (GMV) control of dissolved oxygen (DO) level in a batch bioreactor in which Saccharomyces cerevisiae is produced at aerobic condition. Air flow rate and mixing rate were varied to determine the maximum local liquid phase volumetric mass transfer coefficient (KLa). Maximum KLa value was determined at a mixing rate of 600 rpm and air flow rate of 3.4 Lmin−1. For control purpose, manipulated variable was selected as air flow rate due to its effectiveness on the KLa. To examine the dynamic behavior of the bioreactor, various input signals were utilized as a forcing function and three different model orders were tested. A second0order controlled auto regressive moving average (CARMA) model was used as the process model in the control algorithm and in the system identification step. It is concluded that the ternary input is more suitable than the other input types used in this work for system identification. Recursive least squares method (RLS) was used to determine the model parameters. GMV control results were compared with the traditional PID control results by using performance criteria of IAE and ITAE for different types of DO set point trajectories. DO concentration in the batch bioreactor was controlled more successfully with an adaptive controller structure of GMV than the PID controller with fixed parameters.