Showing papers on "System identification published in 1992"
TL;DR: In this paper, the authors present two algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data, which are classified as one of the subspace model identification schemes.
Abstract: In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme)...
624 citations
TL;DR: This paper addresses the issues related to the identification of nonlinear discrete-time dynamic systems using neural networks with particular attention to the connections between existing techniques for nonlinear systems identification and some aspects of neural network methodology.
Abstract: Many real-world systems exhibit complex nonlinear characteristics and cannot be treated satisfactorily using linear systems theory. A neural network which has the ability to learn sophisticated nonlinear relationships provides an ideal means of modelling complicated nonlinear systems. This paper addresses the issues related to the identification of nonlinear discrete-time dynamic systems using neural networks. Three network architectures, namely the multi-layer perceptron, the radial basis function network and the functional-link network, are presented and several learning or identification algorithms are derived. Advantages and disadvantages of these structures are discussed and illustrated using simulated and real data. Particular attention is given to the connections between existing techniques for nonlinear systems identification and some aspects of neural network methodology, and this demonstrates that certain techniques employed in the neural network context have long been developed by the control e...
618 citations
01 Sep 1992
TL;DR: It is shown how genetic algorithms can be applied for system identification of both continuous and discrete time systems and are effective in both domains and are able to directly identify physical parameters or poles and zeros.
Abstract: It is shown how genetic algorithms can be applied for system identification of both continuous and discrete time systems. It is shown that they are effective in both domains and are able to directly identify physical parameters or poles and zeros. This can be useful because changing one physical parameter might affect every parameter of a system transfer function. The estimates of poles and zeros are then used to design a discrete time pole placement adaptive controller. Simulations for minimum and nonminimum phase systems and a system with unmodeled dynamics are presented. >
538 citations
TL;DR: The model validation problem addressed is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data?
Abstract: The gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data. The model validation problem addressed is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data? This problem is studied for the standard H/sub infinity // mu framework models. A necessary condition for such a model to describe an experimental datum is obtained. For a large class of models in the robust control framework, this condition is computable as the solution of a quadratic optimization problem. >
368 citations
TL;DR: A novel approach is adopted which employs a hybrid clustering and least squares algorithm which significantly enhances the real-time or adaptive capability of radial basis function models.
Abstract: Recursive identification of non-linear systems is investigated using radial basis function networks. A novel approach is adopted which employs a hybrid clustering and least squares algorithm. The recursive clustering algorithm adjusts the centres of the radial basis function network while the recursive least squares algorithm estimates the connection weights of the network. Because these two recursive learning rules are both linear, rapid convergence is guaranteed and this hybrid algorithm significantly enhances the real-time or adaptive capability of radial basis function models. The application to simulated real data are included to demonstrate the effectiveness of this hybrid approach.
359 citations
TL;DR: The elementary MOESP algorithm presented in the first part of this series of papers is analysed and the asymptotic properties of the estimated state-space model when only considering zero-mean white noise perturbations on the output sequence are studied.
Abstract: The elementary MOESP algorithm presented in the first part of this series of papers is analysed in this paper. This is done in three different ways. First, we study the asymptotic properties of the estimated state-space model when only considering zero-mean white noise perturbations on the output sequence. It is shown that, in this case, the MOESPl implementation yields asymptotically unbiased estimates. An important constraint to this result is that the underlying system must have a finite impulse response and subsequently the size of the Hankel matrices, constructed from the input and output data at the beginning of the computations, depends on the number of non-zero Markov parameters. This analysis, however, leads to a second implementation of the elementary MOESP scheme, namely MOESP2. The latter implementation has the same asymptotic properties without the finite impulse response constraint. Secondly, we compare the MOESP2 algorithm with a classical state space model identification scheme. The latter...
300 citations
01 Feb 1992
TL;DR: An attempt is made to organize and survey recent work, and to present it in a unified and accessible form, on the need for a new approach suitable for high-speed processing and the use of difference operators in numerical analysis.
Abstract: An attempt is made to organize and survey recent work, and to present it in a unified and accessible form. The need for a new approach suitable for high-speed processing is discussed in the context of several applications in control and communications, and a historical perspective of the use of difference operators in numerical analysis is presented. The general systems calculus, based on divided-different operators is introduced to unify the continuous-time and discrete-time systems theories. This calculus is then used as a framework to treat the three problems of system state estimation; system identification and time-series modeling; and control system design. Realization aspects of algorithms based on the difference operator representation, including such issues as coefficient rounding and implementation with standard hardware, are also discussed. >
276 citations
TL;DR: In this article, a method to generate exciting identification trajectories in order to minimize the effect of noise and error modeling on the standard least-squares (LS) solution is presented.
Abstract: A common way to identify the inertial parameters of robots is to use a linear model in relation to the parameters and standard least-squares (LS) techniques. This article presents a method to generate exciting identification trajectories in order to minimize the effect of noise and error modeling on the LS solution. Using nonlinear optimization techniques, the condition number of a matrix W obtained from the energy model is minimized, and the scaling of its terms is carried out. An example of a three-degree-of-freedom robot is presented.
273 citations
TL;DR: In this paper, a frequency-response identification technique and a robust control design method are used to set up such an iterative scheme, where each identification step uses the previously designed controller to obtain new data from the plant and the associated identification problem has been solved by means of a coprime factorization of the unknown plant.
Abstract: If approximate identification and model-based control design are used to accomplish a high-performance control system, then the two procedures must be treated as a joint problem. Solving this joint problem by means of separate identification and control design procedures practically entails an iterative scheme. A frequency-response identification technique and a robust control design method are used to set up such an iterative scheme. Each identification step uses the previously designed controller to obtain new data from the plant. The associated identification problem has been solved by means of a coprime factorization of the unknown plant. The technique's utility is illustrated by an example. >
237 citations
TL;DR: In this paper, a class of algorithms for the problem of system identification in ~ are investigated, and conditions in terms of properties of the window functions are derived, which guarantee robust convergence of the algorithms.
204 citations
TL;DR: It is shown that the feedforward network (FFN) pattern learning rule is a first-order approximation of the FFN-batch learning rule, and is valid for nonlinear activation networks provided the learning rate is small.
Abstract: Four types of neural net learning rules are discussed for dynamic system identification. It is shown that the feedforward network (FFN) pattern learning rule is a first-order approximation of the FFN-batch learning rule. As a result, pattern learning is valid for nonlinear activation networks provided the learning rate is small. For recurrent types of networks (RecNs), RecN-pattern learning is different from RecN-batch learning. However, the difference can be controlled by using small learning rates. While RecN-batch learning is strict in a mathematical sense, RecN-pattern learning is simple to implement and can be implemented in a real-time manner. Simulation results agree very well with the theorems derived. It is shown by simulation that for system identification problems, recurrent networks are less sensitive to noise. >
TL;DR: In this article, the problem of deriving so-called hard error bounds for estimated transfer functions is addressed, i.e., the true system Nyquist plot will be confined with certainty to a given region, provided that the underlying assumptions are satisfied.
Abstract: The problem of deriving so-called hard-error bounds for estimated transfer functions is addressed. A hard bound is one that is sure to be satisfied, i.e. the true system Nyquist plot will be confined with certainty to a given region, provided that the underlying assumptions are satisfied. By blending a priori knowledge and information obtained from measured data, it is shown how the uncertainty of transfer function estimates can be quantified. The emphasis is on errors due to model mismatch. The effects of unmodeled dynamics can be considered as bounded disturbances. Hence, techniques from set membership identification can be applied to this problem. The approach taken corresponds to weighted least-squares estimation, and provides hard frequency-domain transfer function error bounds. The main assumptions used in the current contribution are: that the measurement errors are bounded, that the true system is indeed linear with a certain degree of stability, and that there is some knowledge about the shape of the true frequency response. >
TL;DR: A Wiener system, i.e., a system in which a linear dynamic part is followed by a nonlinear and memoryless one, is identified and a nonparametric algorithm recovering the characteristic from input-output observations of the whole system is proposed.
Abstract: A Wiener system, i.e., a system in which a linear dynamic part is followed by a nonlinear and memoryless one, is identified. No parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem, and a nonparametric algorithm recovering the characteristic from input-output observations of the whole system is proposed. Its consistency is shown and the rate of convergence is given. An idea for identification of the impulse response of the linear subsystem is proposed. Results of numerical simulation are also presented. >
TL;DR: A robustly convergent nonlinear algorithm is derived, and bounds on the worst-case identification error (in the H/sub infinity / norm) are obtained.
Abstract: A linear algorithm and a nonlinear algorithm for the problem of system identification in H/sub infinity / posed by Helmicki et al. (1990) for discrete-time systems are presented. The authors derive some error bounds for the linear algorithm which indicate that it is not robustly convergent. However, the worst-case identification error is shown to grow as log(n), where n is the model order. A robustly convergent nonlinear algorithm is derived, and bounds on the worst-case identification error (in the H/sub infinity / norm) are obtained. >
TL;DR: In this article, it was shown that there is no robustly convergent linear algorithm for identifying exponentially stable systems in the presence of noise which is not tuned to prior information about the unknown system or noise.
TL;DR: In this article, the authors proposed a control-relevant identification strategy for a class of long-range predictive controllers and showed that under certain conditions the best process model for predictive control is that which is estimated using an identification objective function that is a dual of the control objective function.
Abstract: The question of a suitable control-relevant identification strategy for a class of long-range predictive controllers is addressed. It is shown that under certain conditions the best process model for predictive control is that which is estimated using an identification objective function that is a dual of the control objective function. The resulting nonlinear least squares calculation is asymptotically equal to a standard recursive least squares with an appropriate (model and controller-dependent) FIR data prefilter. Experimental results demonstrate the validity and practicality of the proposed estimation law. >
TL;DR: Two new lattice-based algorithms for adaptive IIR filtering and system identification are proposed, one a reinterpretation of the Steiglitz-McBride method, and the other a variation on the output error method.
Abstract: Previous attempts at applying lattice structures to adaptive infinite-impulse-response (IIR) filtering have met with gradient computations of O(N/sup 2/) complexity. To overcome this computational burden, two new lattice-based algorithms are proposed for adaptive IIR filtering and system identification, with both algorithms of O(N) complexity. The first algorithm is a reinterpretation of the Steiglitz-McBride method (1965), while the second is a variation on the output error method. State space models are employed to make the derivations transparent, and the methods can be extended to other parameterizations if desired. The set of possible stationary points of the algorithms is shown to be consistent with the convergent points obtained from the direct-form versions of the Steiglitz-McBride and output error methods, whose properties are well studied. The derived algorithms are as computationally efficient as existing direct-form based algorithms, while overcoming the stability problems associated with time-varying direct-form filters. >
TL;DR: In this article, a joint optimization problem is posed which simultaneously solves the plant model estimate and control design, so as to optimize robust performance over the set of plants consistent with a specified experimental data set.
Abstract: A criterion for system identification is developed that is consistent with the intended use of the fitted model for modern robust control synthesis. Specifically, a joint optimization problem is posed which simultaneously solves the plant model estimate and control design, so as to optimize robust performance over the set of plants consistent with a specified experimental data set. >
TL;DR: Strong consistency of the proposed parameter estimators is proved under certain sufficient conditions and the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation.
Abstract: Addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated. It is assumed that the input is non-Gaussian and the noises are Gaussian. The square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation. An optimization algorithm is presented. Strong consistency of the proposed parameter estimators is proved under certain sufficient conditions. Both single-input single-output and multiple-input multiple-output cases are investigated. Finally, simulation results are presented to illustrate the proposed approach. >
TL;DR: The role of linear input-output models in hydrological forecasting is discussed and the algebraic analysis of linear systems with single or multiple input and single output is presented in outline.
TL;DR: In this article, a system identification procedure is proposed to estimate all the derivatives simultaneously, and numerical simulations and reduction of the experimentally obtained direct derivatives are presented, indicating the reliability of the method.
TL;DR: Most processes of realistic complexity cannot be described by simple linear relationships, so an alternative to creating high order/non-linear models is to develop 'composite models’, i.e. a collectio ...
Abstract: Most processes of realistic complexity cannot be described by simple linear relationships. An alternative to creating high order/non-linear models is to develop 'composite models’, i.e. a collectio ...
TL;DR: In this article, the authors consider strongly stabilizable systems for which a strongly stabilizing controller is known approximately, and they consider system identification in the graph, gap, and chordal metrics using robust H/sub infinity / identification of the closed-loop transfer function in the framework proposed by A.J. Helmicki et al.
Abstract: For strongly stabilizable systems for which a strongly stabilizing controller is known approximately, the authors consider system identification in the graph, gap, and chordal metrics using robust H/sub infinity / identification of the closed-loop transfer function in the framework proposed by A.J. Helmicki et al. (1990). Error bounds are derived showing that robust convergence is guaranteed and that the identification can be satisfactorily combined with a model reduction step. Two notions of robust identification of stable systems are compared, and an alternative robust identification technique based on smoothing, which can be used to yield polynomial models directly, is developed. >
TL;DR: In this article, a method of sensor placement for the purpose on-orbit modal identification and test-analysis correlation is presented, which is an extension of the affective Independence method presented in past work to include the effects of a general representation of measurement noise.
Abstract: A method of sensor placement for the purpose on-orbit modal identification and test-analysis correlation is presented. The method is an extension of the affective Independence method presented in past work to include the effects of a general representation of measurement noise. Sensor noise can be distributed nonuniformly throughout the structure as well as correlated between sensors. The only restriction is that the corresponding noise covariance intensity matrix is positive definite
TL;DR: In this paper, the authors proposed a new control design methodology for distributed systems with unknown nonlinear dynamics, where the convergence to an asymptotically stable equilibrium point after a small-amplitude transient disturbance quickly approaches an invariant manifold W which is locally tangent to the eigenspace of the slow modes and is hence of the same dimension.
Abstract: We propose a new control design methodology for distributed systems with unknown nonlinear dynamics. The approach is appropriate for systems whose linearized differential operator possesses an eigenspectrum that can be partitioned into a low-dimensional slow spectrum and an infinite-dimensional fast complement. This separation of time scales allows us to utilize center manifold and normal form techniques of modern geometric theories for dynamical systems. It is shown that the convergence to an asymptotically stable equilibrium point after a small-amplitude transient disturbance quickly (exponentially fast) approaches an invariant manifold W which is locally tangent to the eigenspace of the slow modes and is hence of the same dimension. The nonlinear dynamics on this invariant manifold is much slower than the fast approach and is dominated by the slow modes with the fast modes coupled “adiabatically” to them. The convergence can hence be best accelerated using a slow control with smooth nonlinear feedback involving only the slow modes. Nonlinear feedback is shown to drastically improve the performance of linear feedback. The only required information about the system in our approach is the slow adjoint eigenfunctions which can be easily estimated with a Karhunen-Loeve scheme for distributed systems. This identification scheme is quite robust to changes in process dynamics and can hence be carried out on-line in parallel with feedback control. The overall approach is verified by numerical experiments.
TL;DR: A study of existing OBE algorithms, with a particular interest in the tradeoff between algorithm performance interpretability and convergence properties, suggests that an interpretable, converging UOBE algorithm will be found.
Abstract: : A quite general class of Optimal Bounding Ellipsoid (OBE) algorithms including all methods published to date, can be unified into a single framework called the Unified OBE (UOBE) algorithm. UOBE is based on generalized weighted recursive least squares in which very broad classes of 'forgetting factors' and data weights may be employed. Different instances of UOBE are distinguished by their weighting policies and the criteria used to determine their optimal values. A study of existing OBE algorithms, with a particular interest in the tradeoff between algorithm performance interpretability and convergence properties, is presented. Results suggest that an interpretable, converging UOBE algorithm will be found. In this context, a new UOBE technique, the set membership stochastic approximation (SM-SA) algorithm is introduced. SM-SA possesses interpretable optimization measures and known conditions under which its estimator will converge.
TL;DR: In this paper, a predictive control strategy based on state-space models is proposed for industrial processes, where the control calculation is based on a general performance index and parameterization of the control variables in a nonlinear model.
01 Jan 1992
TL;DR: Two new subspace algorithms for identifying mixed deterministic-stochastic systems are derived and these state sequences are shown to be outputs of nonsteady-state Kalman filter banks.
Abstract: Two new subspace algorithms for identifying mixed deterministic-stochastic systems are derived. Both algorithms determine state sequences through the projection of input and output data. These state sequences are shown to be outputs of nonsteady-state Kalman filter banks. From these it is easy to determine the state space system matrices. The algorithms are always convergent (noninterative) and numerically stable since they only make use of QR and singular value decompositions. The two algorithms are similar, but the second one trades off accuracy for simplicity. An example involving a glass oven is considered. >