System Identification Problem Research Articles

The filtering-based recursive least squares identification and convergence analysis for nonlinear feedback control systems with coloured noises

The coloured noise is ubiquitous in industrial processes. This paper addresses the identification problem for the nonlinear feedback systems with coloured noise. Firstly, a direct identification scheme based on the least squares principle is developed to estimate the whole parameters of the nonlinear feedback systems and the convergence analysis is carried out through the stochastic stability theory. Secondly, for the purpose of improving the estimation accuracy, a filtering-based identification framework is proposed by constructing a linear filter for filtering the input data, output data and the coloured noise, and the coloured noise is transformed into a white noise. This identification scheme based on the filtering technique can effectively reduce the adverse effects caused by coloured noise and parameter estimation accuracy is enhanced compared with the direct least squares algorithm. Meanwhile, the convergence analysis of the filtering-based identification algorithm is given to provide a theoretical analysis. Finally, the simulation example is carried out by performance test and comparison analysis and simulation results show the effectiveness of the proposed identification methods.

Asymptotically efficient Quasi-Newton type identification with quantized observations under bounded persistent excitations

This paper is concerned with the optimal identification problem of dynamical systems in which only quantized output observations are available under the assumption of fixed thresholds and bounded persistent excitations. Based on a time-varying projection, a weighted Quasi-Newton type projection (WQNP) algorithm is proposed. With some mild conditions on the weight coefficients, the algorithm is proved to be mean square and almost surely convergent, and the convergence rate can be the reciprocal of the number of observations, which is the same order as the optimal estimate under accurate measurements. Furthermore, inspired by the structure of the Cramér–Rao lower bound, an information-based identification (IBID) algorithm is constructed with an adaptive design about weight coefficients of the WQNP algorithm, where the weight coefficients are related to the parameter estimates which leads to the essential difficulty of algorithm analysis. Beyond the convergence properties, this paper demonstrates that the IBID algorithm tends asymptotically to the Cramér–Rao lower bound, and hence is asymptotically efficient. A numerical example is simulated to show the effectiveness of the proposed algorithms.

Kalman Filter Using a Third-Order Tensorial Decomposition of the Impulse Response

For system identification problems associated with long-length impulse responses, the recently developed decomposition-based technique that relies on a third-order tensor (TOT) framework represents a reliable choice. It is based on a combination of three shorter filters, which merge their estimates in tandem with the Kronecker product. In this way, the global impulse response is modeled in a more efficient manner, with a significantly reduced parameter space (i.e., fewer coefficients). In this paper, we further develop a Kalman filter based on the TOT decomposition method. As compared to the recently designed recursive least-squares (RLS) counterpart, the proposed Kalman filter achieves superior performance in terms of the main criteria (e.g., tracking and accuracy). In addition, it significantly outperforms the conventional Kalman filter, while also having a lower computational complexity. Simulation results obtained in the context of echo cancellation support the theoretical framework and the related advantages.

Identification of Wiener state–space models utilizing Gaussian sum smoothing

In this paper, we address the problem of system identification for Wiener state–space models. Our approach is based on the Maximum Likelihood method and the Expectation–Maximization algorithm. In the problem of interest, we model the output nonlinearity as a piecewise polynomial function and we jointly estimate the parameters of the linear system with the coefficients of each polynomial section. In our proposal, the computation of the cost function in the Expectation–Maximization algorithm requires the computation of the joint distribution of the state and the output of the linear system given the output of the nonlinear block. These quantities are obtained from an approximation that leads to a novel Gaussian sum smoothing algorithm. Additionally, we show that our method also addresses the identification of state–space systems in which the output is produced by a known quantizer. We present numerical examples to illustrate the benefits of the proposed identification technique.

Statistically consistent inverse optimal control for discrete-time indefinite linear–quadratic systems

The Inverse Optimal Control (IOC) problem is a structured system identification problem that aims to identify the underlying objective function based on observed optimal trajectories. This provides a data-driven way to model experts’ behavior. In this paper, we consider the case of discrete-time finite-horizon linear–quadratic problems where: the quadratic cost term in the objective is not necessarily positive semi-definite; the planning horizon is a random variable; we have both process noise and observation noise; the dynamics can have a drift term; and where we can have a linear cost term in the objective. In this setting, we first formulate the necessary and sufficient conditions for when the forward optimal control problem is solvable. Next, we show that the corresponding IOC problem is identifiable. Using the conditions for existence of an optimum of the forward problem, we then formulate an estimator for the parameters in the objective function of the forward problem as the globally optimal solution to a convex optimization problem, and prove that the estimator is statistical consistent. Finally, the performance of the algorithm is demonstrated on two numerical examples.

Joint input–output identification of unstable systems with kernel regularization

This paper discusses closed-loop identification of unstable systems. In particular, we first apply the joint input–output identification method and then convert the identification problem of unstable systems into that of stable systems, which can be tackled by using kernel-based regularization methods. We propose to identify two transfer functions by kernel regularization, the one from the reference signal to the input, and the one from the reference signal to the output. Since these transfer functions are stable, kernel regularization methods can construct their accurate models. Then the model of unstable system is constructed by ratio of these functions. The effectiveness of the proposed method is demonstrated by a numerical example and a practical experiment with a DC motor.

Constrained Normalized Subband Adaptive Filter Algorithm and Its Performance Analysis

AbstractConstrained least mean square (CLMS) algorithm is the most popular constrained adaptive filtering algorithm due to its simple structure and easy implementation. However, its convergence slows down when the input signal is colored. To address this issue, this paper firstly introduces the normalized subband adaptive filter (NSAF) into the constrained filtering problem and derives a constrained NSAF (CNSAF) algorithm using the Lagrange multiplier method. Benefiting from the good decorrelation capability of the NSAF, the proposed CNSAF algorithm significantly improves the convergence performance of the CLMS algorithm under colored inputs. Then, the mean and mean-square stability of the CNSAF algorithm is analyzed, and the theoretical models to characterize the transient and steady-state mean square deviation (MSD) behaviors of the CNSAF algorithm are derived utilizing the Kronecker product property and vectorization method. Further to extend the CNSAF algorithm to the problem of sparse system identification, a sparse version of the CNSAF algorithm (S-CNSAF) is derived. Finally, the validity of the derived theoretical MSD prediction models and the superiority of the proposed algorithms are confirmed by extensive computer simulations on system identification with colored inputs.

State Observer-Based Conditioned Reverse-Path Method for Nonlinear System Identification

In light of the complex behavior of vibrating structures, their reliable modeling plays a crucial role in the analysis and system design for vibration control. In this paper, the reverse-path (RP) method is revisited, further developed, and applied to modeling a nonlinear system, particularly with respect to the identification of the frequency response function for a nominal underlying linear system and the determination of the structural nonlinearities. The present approach aims to overcome the requirement for measuring all nonlinear system states all the time during operation. Especially in large-scale systems, this might be a tedious task and often practically infeasible since it would require having individual sensors assigned for each state involved in the design process. In addition, the proper placement and simultaneous operation of a large number of transducers would represent further difficulty. To overcome those issues, we have proposed state estimation in light of the observability criteria, which significantly reduces the number of required sensor elements. To this end, relying on the optimal sensor placement problem, the state estimation process reduces to the solution of Kalman filtering. On this ground, the problem of nonlinear system identification for large-scale systems can be addressed using the observer-based conditioned RP method (OBCRP) proposed in this paper. In contrast to the classical RP method, the current one can potentially handle local and distributed nonlinearities. Moreover, in addition to the state estimation and in comparison to the orthogonal RP method, a new frequency-dependent weighting is introduced in this paper, which results in superior nonlinear system identification performances. Implementation of the method is demonstrated on a multi-degree-of-freedom discretized lumped mass system, representing a substitute model of a physical counterpart used for the identification of the model parameters.

Output-only identification of time-varying structural modal parameters under thermal environment

Obtaining the input load presents a significant challenge for system identification problems with time-varying characteristics in aerospace engineering. Therefore, the modal parameter is determined through output-only identification techniques. Considering rapid time-varying characteristics in thermal environment, a Recursive Subspace Method (RSM) is used to enhance the precision of identifying modal parameters. A three-degree-of-freedom system with time-varying stiffness is first investigated to validate the identification method. The effect of noise on the robustness of the algorithm is discussed. Then, the experimental investigation is undertaken considering a composite beam under a time-varying thermal environment though the thermal-vibration experimental system. Experimental results indicate that the change of structural modal frequencies under variable temperature environment is mainly affected by the thermal stress induced in the structure. Comparing the experimental and simulation result, the output-only identification approach has good efficiency and convergence for time-varying system.

Joint learning of linear time-invariant dynamical systems

Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related systems to estimate their transition matrices more accurately. To address this problem, we investigate methods for jointly estimating the transition matrices of multiple systems. It is assumed that the transition matrices are unknown linear functions of some unknown shared basis matrices. We establish finite-time estimation error rates that fully reflect the roles of trajectory lengths, dimension, and number of systems under consideration. The presented results are fairly general and show the significant gains that can be achieved by pooling data across systems, in comparison to learning each system individually. Further, they are shown to be robust against moderate model misspecifications. To obtain the results, we develop novel techniques that are of independent interest and are applicable to similar problems. They include tightly bounding estimation errors in terms of the eigen-structures of transition matrices, establishing sharp high probability bounds for singular values of dependent random matrices, and capturing effects of misspecified transition matrices as the systems evolve over time.

Blind instrument response function identification from fluorescence decays

Time-resolved fluorescence spectroscopy plays a crucial role when studying dynamic properties of complex photochemical systems. Nevertheless, the analysis of measured time decays and the extraction of exponential lifetimes often requires either the experimental assessment or the modeling of the instrument response function (IRF). However, the intrinsic nature of the IRF in the measurement process, which may vary across measurements due to chemical and instrumental factors, jeopardizes the results obtained by reconvolution approaches. In this paper, we introduce a novel methodology, called blind instrument response function identification (BIRFI), which enables the direct estimation of the IRF from the collected data. It capitalizes on the properties of single exponential signals to transform a deconvolution problem into a well-posed system identification problem. To delve into the specifics, we provide a step-by-step description of the BIRFI method and a protocol for its application to fluorescence decays. The performance of BIRFI is evaluated using simulated and time-correlated single-photon counting data. Our results demonstrate that the BIRFI methodology allows an accurate recovery of the IRF, yielding comparable or even superior results compared with those obtained with experimental IRFs when they are used for reconvolution by parametric model fitting.

Wiener Filter Using the Conjugate Gradient Method and a Third-Order Tensor Decomposition

In linear system identification problems, the Wiener filter represents a popular tool and stands as an important benchmark. Nevertheless, it faces significant challenges when identifying long-length impulse responses. In order to address the related shortcomings, the solution presented in this paper is based on a third-order tensor decomposition technique, while the resulting sets of Wiener–Hopf equations are solved with the conjugate gradient (CG) method. Due to the decomposition-based approach, the number of coefficients (i.e., the parameter space of the filter) is greatly reduced, which results in operating with smaller data structures within the algorithm. As a result, improved robustness and accuracy can be achieved, especially in harsh scenarios (e.g., limited/incomplete sets of data and/or noisy conditions). Besides, the CG-based solution avoids matrix inversion operations, together with the related numerical and complexity issues. The simulation results are obtained in a network echo cancellation scenario and support the performance gain. In this context, the proposed iterative Wiener filter outperforms the conventional benchmark and also some previously developed counterparts that use matrix inversion or second-order tensor decompositions.

Artificial Ecosystem Optimizer-Based System Identification and Its Performance Evaluation

AbstractThis study delves into the realm of system identification, a crucial sub-field in control engineering, aimed at constructing mathematical models of systems based on input/output data. This work particularly proposes the application of artificial ecosystem algorithm (AEO) for solving system identification problems. Inspired by the energy flow of natural ecosystems, AEO has undergone specific modifications leading to derived versions. Additionally, five diverse meta-heuristic algorithms are employed to assess their applicability and performance in system identification using data from an air stream heater experiment kit. A comprehensive performance comparison is made, considering time bounds, maximum generations, early stopping, and function evaluation constraints, presenting their respective performances. Among the evaluated algorithms, the AEO algorithm enhanced with the sine and cosine strategy stands out with a determined R2 value of 0.951. This algorithm consistently outperforms others in Wilcoxon tests, showcasing its significant success. Our study affirms that meta-heuristic algorithms, particularly the proposed AEO algorithm, can be effectively applied to system identification problems, yielding successful calculations of transfer function parameters.

Reduced order infinite impulse response system identification using manta ray foraging optimization

This article presents a useful application of the Manta Ray Foraging Optimization (MRFO) algorithm for solving the adaptive infinite impulse response (IIR) system identification problem. The effectiveness of the proposed technique is validated on four benchmark IIR models for reduced order system identification. The stability of the proposed estimated IIR system is assured by incorporating a pole-finding and initialization routine in the search procedure of the MRFO algorithm and this algorithmic modification contributes to the MRFO algorithm when seeking stable IIR filter solutions. The absence of such a scheme, which is primarily the case with the majority of the recently published literature, may lead to the generation of an unstable IIR filter for unknown real-world instances (particularly when the estimation order increases). Experiments conducted in this study highlight that the proposed technique helps to achieve a stable filter even though large bounds for the design variables are considered. The convergence rate, robustness, and computational speed of MRFO for all the considered problems are investigated. The influence of the control parameters of MRFO on the design performances is evaluated to gain insight into the interaction between the three foraging strategies of the algorithm. Extensive statistical performance analyses employing various non-parametric hypothesis tests concerning the design consistency and convergence are conducted for comparison of the proposed MRFO-based approach with six other metaheuristic search procedures to investigate the efficiency. The results on the mean square error metric also highlight the improved solution quality of the proposed approach compared to the various techniques published in the literature.

Distributionally robust system identification for continuous fermentation nonlinear switched system under moment uncertainty of experimental data

In this paper, we consider a nonlinear switched dynamical system (NSDS) with unknown system parameters in the context of uncertain experimental data. This system is employed to model the continuous fermentation for the production of 1,3-propanediol through glycerol bioconversion. The uncertain experimental data points are regarded as stochastic variables and only their first-order moment information of the probability distributions is available. The target of this paper is to optimize these system parameters under the environment of uncertain experimental data. Taking these factors into account, we propose a distributionally robust system identification (DRSI) problem (i.e., a bi-level system identification problem) governed by the NSDS. The objective functional comprises two level objectives: (i) the inner-level objective aims to maximize the expectation of the relative error between the solution of the NSDS and the uncertain experimental data with respect to their probability distributions at approximately stable time; and (ii) the outer-level objective is to minimize the expectation with respect to these system parameters. The DRSI problem is equivalently transformed into a single-level system identification (SLSI) problem with non-smooth term through the application of the duality theory in the probability space. A smoothing technique is employed to approximate the non-smooth term in the SLSI problem. Subsequently, an error analysis of the employed smoothing technique is derived. The gradients of the objective functional in the SLSI with respect to these system parameters are obtained. An optimization algorithm is designed to solve the SLSI problem. Finally, the paper concludes with simulation results.

Binary observation‐based FIR system identification under sequence denial of service attacks

AbstractDue to the close interaction between computing, sensing, communication, and driving of the cyber‐physical system (CPS), which makes it highly vulnerable to cyber attacks, the security of CPS has attracted wide attention. In the article, we discuss the system identification problem of the finite impulse response system under sequence denial of service attacks. The identification algorithm of the unknown parameter is designed under binary observations, and its convergence performance is analyzed. The optimal attack strategy problem is modeled as a optimized problem with constraints based on the covariance matrix of estimation error, the solution method and implementation algorithm are given. From the perspective of the defender, an encryption‐type defense algorithm is designed, and then the optimal defense strategy is presented. The numerical simulation is used to verify the validity of the proposed method.

A New Method for Dynamical System Identification by Optimizing the Control Parameters of Legendre Multiwavelet Neural Network

Wavelet neural networks have been widely applied to dynamical system identification fields. The most difficult issue lies in selecting the optimal control parameters (the wavelet base type and corresponding resolution level) of the network structure. This paper utilizes the advantages of Legendre multiwavelet (LW) bases to construct a Legendre multiwavelet neural network (LWNN), whose simple structure consists of an input layer, hidden layer, and output layer. It is noted that the activation functions in the hidden layer are adopted as LW bases. This selection if based on the its rich properties of LW bases, such as piecewise polynomials, orthogonality, various regularities, and more. These properties contribute to making LWNNs more effective in approximating the complex characteristics exhibited by uncertainties, step, nonlinear, and ramp in the dynamical systems compared to traditional wavelet neural networks. Then, the number of selection LW bases and the corresponding resolution level are effectively optimized by the simple Genetic Algorithm, and the improved gradient descent algorithm is implemented to learn the weight coefficients of LWNN. Finally, four nonlinear dynamical system identification problems are applied to validate the efficiency and feasibility of the proposed LWNN-GA method. The experiment results indicate that the LWNN-GA method achieves better identification accuracy with a simpler network structure than other existing methods.

Parameter identification of the linear discrete-time stochastic systems with unknown exogenous inputs

The paper addresses a parameter identification problem for linear discrete-time stochastic systems with unknown exogenous inputs. Such systems are considered when solving practical problems related to the measurements processing in the case when it is impossible to do any assumptions about the evolution of unknown input signal or its statistical characteristics that can change over time. We consider a class of discrete time linear stochastic systems with unknown exogenous inputs, where an additional source of a priori uncertainty of the system model is introduced, namely, the unknown parameter, on the elements of which the system model matrices can depend. This formulation of the parameter identification problem under the conditions of unknown inputs and the presence of random noises describes a high degree of uncertainty of a discrete time linear stochastic system. We propose a novel solution to this problem based on the construction of a new instrumental identification criterion. Minimization of this criterion allows for evaluating the unknown system model parameters simultaneously with the estimating of the state vector and unknown exogenous inputs of the system. Numerical experiments confirm the validity and efficiency of the proposed parameter identification method.

An atom search optimization approach for IIR system identification

ABSTRACT Filtering, or digital signal processing, is a significant and fundamental requirement in fields such as signal systems and computers. The process of designing optimal digital filters is difficult, which has led researchers to design filters using emerging evolutionary computations. Metaheuristics have emerged as the most promising tool for solving optimization problems, with excellent development and improvement. However, it has not been clear how to select the best performing metaheuristic to design an optimal digital filter. In this paper, a digital infinite impulse response (IIR) filter is constructed using the atom search optimization (ASO) algorithm impressed by the physical motion of atoms in nature based on molecular dynamics. The simulation results obtained are extensively compared with the results of other optimization algorithms such as moth flame optimization, gravitational search algorithm and artificial bee colony optimization. ASO was found to have the highest percentage of improvement. Furthermore, eight cases are analyzed across four numerical filter instances with the same degree and four with reduced degree, and the results are validated by outperforming several different algorithm-based approaches in the literature. The stability analysis on the basis of pole zero diagrams further cements the efficacy of the ASO for IIR system identification problem.

Analysis of the Least Mean Square algorithm with processing delays in the adaptive arm for Gaussian inputs for system identification

This paper analyzes the effect of a processing delay on the Least Mean Squares (LMS) algorithm for a system identification problem when the processing delay is in the adaptive arm of the filter. Thus the sensing of the input signal is delayed. The input is assumed to be a zero mean stationary Gaussian process. The theoretical mean and mean square behavior of the adaptive weight vector is analyzed. The weight vector is shown to be biased and significantly affects the mean square deviation (MSD). Monte Carlo simulations are presented in support of the assumptions used to derive the theoretical model as a function of the delay, bandwidth and step-size for the LMS algorithm. The results suggest bias problems with other more complicated adaptive filtering algorithms such as Normalized LMS and Recursive Least Squares.