Identification Of Linear Dynamic Systems Research Articles

Identification of linear dynamic systems using the artificial bee colony algorithm

This paper presents an investigation into the development of system identification using the artificial bee colony (ABC) algorithm. A system identification task can be formulated as an optimization problem where the objective is to obtain a model and a set of parameters that minimize the prediction error between the measured plant outputs and the model outputs. The most common existing system identification approaches, such as the recursive least squares method and autoregressive exogenous method, are substantially analytical and based on a mathematical derivation of the system's model. Evolutionary computation, which seems to be a very promising approach, is an alternative to these methods because a little knowledge about the problem is sufficient in this approach and it can be easily combined with many other techniques from artificial intelligence, control engineering, machine learning, and so on. In this paper, an evolutionary approach for system identification is considered and attempted to demonstrate how the ABC algorithm can be applied in system identification tasks. Mathematical models of dynamic systems are obtained using difference equations represented in discrete time and the ABC algorithm is used to estimate the unknown parameters of the systems. Simulation results demonstrate that the proposed linear system identification method has good identification performance. Moreover, this method is applied to the identification of a direct current motor in order to show the performance of the ABC algorithm. The obtained results show that the identified and actual plant outputs successfully match each other.

Enforcing stability constraints in set-membership identification of linear dynamic systems

In this paper, we consider the identification of linear systems, a priori known to be stable, from input–output data corrupted by bounded noise. By taking explicitly into account a priori information on system stability, a formal definition of the feasible parameter set for a stable linear system is provided. On the basis of a detailed analysis of the geometrical structure of the feasible set, convex relaxation techniques are presented to solve nonconvex optimization problems arising in the computation of parameter uncertainty intervals. Properties of the computed relaxed bounds are discussed. A simulated example is presented to show the effectiveness of the proposed technique.

Random Decrement Technique Based on the Sampling Methods

This paper presents the random decrement (RD) technique based on the sampling method for parameter identification of linear dynamic system. The development of RD technique was elaborated briefly in the aspects of identifying the dynamic properties, and then this paper summarized the corresponding parameters recognition problems due to the quantity and quality of measured sampling segments. Detailed analysis of two kinds of sampling method (the probability-proportional-to-size and two-stage sampling) is conducted to investigate its adaptation range in extracting RD signatures. The results of two simulated examples indicates that in view of the different vibration parameter recognition situation, the above provided RD technique based on different sampling methods could improve the quality of RD signature obviously, and lead to a quite accurate frequency and the damping ratio of structural system under the effective use of all measured sampling segments.

A quadratic programming-based method for quantized system identification

AbstractThis paper proposes a quadratic programming (QP)-based method, for linear dynamic system identification from quantized data or binary measurements. The main idea of the proposed method is to reformulate the identification problem for finite impulse (FIR) systems, usually viewed as a nonlinear estimation problem with discontinuous nonlinearities, in the form of a standard QP problem, which is a convex optimization problem and can be solved efficiently. The QP-based method is equally applicable to both quantized data and binary measurements without any modification. It has no special assumptions on the identification experiments. An iterative QP-based method is also developed for the identification of infinite impulse response (IIR) systems. Numerical examples demonstrate the effectiveness of the proposed method.

Improved parameter bounds for set‐membership EIV problems

AbstractIn this paper, we consider the set‐membership error‐in‐variables identification problem, that is the identification of linear dynamic systems when output and input measurements are corrupted by bounded noise. A new approach for the computation of parameters uncertainty intervals is presented. First, the problem is formulated in terms of nonconvex optimization. Then, a relaxation procedure is proposed to compute parameter bounds by means of semidefinite programming techniques. Finally, accuracy of the estimate and computational complexity of the proposed algorithm are discussed. Advantages of the proposed technique with respect to previously published ones are discussed both theoretically and by means of a simulated example. Copyright © 2010 John Wiley & Sons, Ltd.

Linear Dynamic System Identification in the Frequency Domain Using Fractional Derivatives

Linear Dynamic System Identification in the Frequency Domain Using Fractional DerivativesThis paper presents a study of the Fourier transform method for parameter identification of a linear dynamic system in the frequency domain using fractional differential equations. Fundamental definitions of fractional differential equations are briefly outlined. The Fourier transform method of identification and their algorithms are generalized so that they include fractional derivatives and integrals.

Inverse spectral problems of the theory of identification of linear dynamic systems

The problem of restoration of the parameters of the linear operator from a finite set of eigenvalues was considered. A new scheme of its solution was proposed, both the necessary and sufficient conditions for existence of solutions were presented, and a procedure of their numerical construction was substantiated. Consideration was given to the applied problems of identification and controllability of the linear dynamic systems.

Identification of linear dynamic systems operating in a networked environment

This paper studies a networked system identification problem, which aims at identifying mathematical models required in networked control/estimation/filtering systems. Specifically, we consider the off-line identification of open-loop stable linear time-invariant processes working in a networked environment. In the networked environment, how the actuators (D/A conversion) operate plays a key role in the complexity of the related identification problems. In particular, it is reasonable to consider the configuration of event-driven actuators subject to random network-induced delays and packet dropouts; as a result, the networked identification problem is formulated as the one to identify continuous-time linear time-invariant models, based on the general non-uniformly non-synchronized sampled data. A modified version of the simplified refined instrumental variable method is proposed to solve this problem, and is validated in a networked identification experiment based on the Matlab/Simulink simulator TrueTime.

Bootstrapped Total Least Squares estimator using (circular) overlap for Errors-In-Variables identification

The identification of linear dynamic system in a frequency domain Errors-In-Variables (EIV) framework often assumes the knowledge of a nonparametric noise model prior to parametric identification. This noise model can be extracted for periodic excitations using various sample mean/sample variance techniques starting from at least P = 4measured periods. The use of overlap and circular-overlap methods were recently introduced to increase the efficiency of the sample maximum likelihood (SML) estimator. This enabled halving the number of required periods while maintaining the efficiency loss of 1.46dB for P = 2 periods with respect to Maximum Likelihood (ML) estimates with known covariance matrix. In this paper, the overlap and circular-overlap methods are applied to the sample BTLS method. A Monte Carlo analysis on a typical low-pass system shows that the efficiency loss with respect to the ML is only 0.12dB when P = 2 periods are available. In addition, the example shows that the efficiency loss for P = 1.2 periods is smaller than the loss introduced by the circular-overlap SML with P = 4 periods.

General Realization Algorithm for Modal Identification of Linear Dynamic Systems

The general realization algorithm (GRA) is developed to identify modal parameters of linear multi-degree-of-freedom dynamic systems subjected to measured (known) arbitrary dynamic loading from known initial conditions. The GRA extends the well known eigensystem realization algorithm (ERA) based on Hankel matrix decomposition by allowing an arbitrary input signal in the realization algorithm. This generalization is obtained by performing a weighted Hankel matrix decomposition, where the weighting is determined by the loading. The state-space matrices are identified in a two-step procedure that includes a state reconstruction followed by a least-squares optimization to get the minimum prediction error for the response. The statistical properties (i.e., bias, variance, and robustness to added output noise introduced to model measurement noise and modeling errors) of the modal parameter estimators provided by the GRA are investigated through numerical simulation based on a benchmark problem with nonclassical damping.

On strong consistency of a class of recursive stochastic Newton-Raphson type algorithms with application to robust linear dynamic system identification

The recursive stochastic algorithms for estimating the parameters of linear discrete-time dynamic systems in the presence of disturbance uncertainty has been considered in the paper. Problems related to the construction of min-max optimal recursive algorithms are demonstrated. In addition, the robustness of the proposed algorithms has been addressed. Since the min-max optimal solution cannot be achieved in practice, an approximate optimal solution based on a recursive stochastic Newton-Raphson type procedure is suggested. The convergence of the proposed practically applicable robustified recursive algorithm is established theoretically using the martingale theory. Both theoretical and experimental analysis related to the practical robustness of the proposed algorithm are also included. .

Sequential Identification of Linear Dynamic Systems with Memory

This paper presents a sequential estimator for some unknown parameters in stochastic linear systems with memory. As examples stochastic differential equations with time delayed drift are considered. Based on the maximum likelihood method, we construct an estimation procedure with given accuracy in the sense of the Lp-norm (p≥ 2). It is shown, that this procedure works also in certain cases, when the normalized information matrix of the observed process is asymptotically degenerated. The almost surely consistency of the proposed estimators and the asymptotic behavior of the length of observations are derived.

A genetic approach to the identification of linear dynamical systems with static nonlinearities

This paper investigates the use of genetic algorithms in the identification of linear systems with static nonlinearitites. Linear systems with static nonlinearities at the input known as the Hammerstein model, and linear systems with static nonlinearities at the output known as the Wiener model are considered in this paper. The parameters of the Hammerstein and the Wiener models are estimated using genetic algorithms from the input-output data by minimizing the error between the true model output and the identified model output. Using genetic algorithms, the Hammerstein and the Wiener models with known nonlinearity structure and unknown parameters can be identified. Moreover, systems with non-minimum phase characteristics can be identified. Extensive simulations have been used to study the convergence properties of the proposed scheme. Simulation examples are included to demonstrate the effectiveness and robustness of the proposed identification scheme.

A Structure Theory for Linear Dynamic Errors-in-Variables Models

We deal with problems connected with the identification of linear dynamic systems in situations when inputs and outputs may be contaminated by noise. The case of uncorrelated noise components and the bounded noise case is considered. If also the inputs may be contaminated by noise, a number of additional complications in identification arise, in particular the underlying system is not uniquely determined from the population second moments of the observations. A description of classes of observationally equivalent systems is given, continuity properties of mappings relating classes of observationally equivalent systems to the spectral densities of the observations are derived and the classes of spectral densities corresponding to a given maximum number of outputs are studied.

Counterexample to General Consistency of Subspace System Identification Methods

Subspace methods for identification of linear dynamical systems consist of two main steps. First, a so-called subspace estimate is constructed. This usually corresponds to estimating the range space of the extended observability matrix. Then, the system parameters are estimated from the subspace estimate. The main objective of this paper is to show that subspace methods for the identification of combined deterministic and stochastic systems may fail to provide a consistent estimate of the subspace. Hence, for certain systems, the transfer function model estimated using the subspace identification algorithms is not a consistent estimate of the true system.

On Consistency of Subspace System Identification Methods

System identification of linear dynamical systems using so-called subspace methods consists of two main steps, First, a signal subspace estimate is found. This usually corresponds to estimating the range space of the extended observability matrix. Then the system parameters are estimated from the subspace estimate. The main result of this note is explicit excitation conditions on the input signals, which guarantee consistent estimates of the range space of the extended observability matrix.

Periodic Excitation for Identification of Dynamic Errors-In-Variables Systems Operating in Closed Loop

A consistent algorithm for identification of linear dynamic systems from noisy input and output measurements is presented under the assumption that the system is excited by an unknown periodic signal with a known period time. The required noise assumptions are weak and the input and output noises are allowed to be fully correlated. The algorithm is suited to identify both stable and unstable systems operating in closed loop.

Adaptive neural control with stable learning

Abstract The paper considers the problem of training on-line a neural network model of non-linear heater battery for implementation in a model-based control scheme. A stable learning scheme is proposed which reduces parameter drift due to process-model mismatch in radial basis function (RBF) networks. A network of pre-defined structure is trained and shown to exhibit finite model mismatch errors, which can produce parameter drift or “de-training” of the network, resulting in inferior control performance. A deadzone approach, similar to ones used in linear dynamic system identification, is applied to RBF network adaption, successfully reducing the degree of “de-training”. The learning scheme is used in a neural controller which is capable of compensating for plant non-linearities, and adapting on-line to degradation in the plant. Experimental results are presented which have been obtained from a flow-controlled heating coil, on a full-size air conditioning plant at the UK Building Research Establishment.

Identification of linear dynamic systems using piecewise constant excitations: Use, misuse and alternatives

Time domain identification of linear dynamic systems using discrete time models relies heavily on the use of piecewise constant excitation signals (ZOH-assumption). If this assumption is not met, severe errors can be generated and the results can be useless. In this article we study the implications of the ZOH-assumption and an alternative is formulated. This leads to frequency domain identification methods based on the band limited assumption (that the signals obey the Shannon sampling theory). The theory and practical aspects of both approaches are compared. Finally, it will be shown that periodic excitations (or perturbation signals) can offer significant advantages in both approaches.

Information-Based Complexity and Nonparametric Worst-Case System Identification

In this paper we review recent results on nonparametric approaches to identification of linear dynamic systems, under nonprobabilistic assumptions on measurement uncertainties. Two main categories of problems are considered in the paper: H ∞ and l 1 settings. The H ∞ setting assumes that the true system is linear time-invariant and the available information is represented by samples of the frequency response of the system, corrupted by an l ∞-norm bounded noise. The aim is to estimate a proper, stable finite-dimensional model. The estimation error is quantified according to an H ∞ norm, measuring the "distance" of the estimated model from the worst-case system in the class of allowable systems, for the worst-case realization of the measurement error. In the l 1 setting, the aim is to identify the samples of the impulse response of an unknown linear time-invariant system. The available information is given by input/output measurements corrupted by l ∞-bounded noise and the estimation error is measured according to an l 1 norm, for the worst case with respect to allowable systems and noise. In this paper, the main results available in the literature for both settings are reviewed, with particular attention to (a) evaluation of the diameter of information under various experimental conditions, (b) convergence to zero of the diameter of information (i.e., existence of robustly convergent identification procedures), and (c) computation of optimal and almost-optimal algorithms. Some results are also reported for the l ∞ setting, similar to the l 1 setting, with the exception of the estimation error, which is measured by an l ∞ norm.