System Identification - General Aspects and Structure

In this chapter, we describe an important class of engineering problem called system identification which is an essential requirement for obtaining models of system of concern that would be necessary for controlling, analyzing the systems. The system identification problem is essentially to pick up the best model out of the several candidate models. Thus, the problem of system identification or modeling building turns out to be an optimization problem. The chapter explain what are different evolutionary computing techniques used in the past and the state- of the art technologies on evolutionary computation. Then, some case studies have been included how the system identification of a number of complex systems effectively achieved by employing these evolutionary computing techniques.

In this paper, we review several lines of recent work aimed at developing practical methods for adaptive on-line stimulus generation for sensory neurophysiology. We consider various experimental paradigms where on-line stimulus optimization is utilized, including the classical optimal stimulus paradigm where the goal of experiments is to identify a stimulus which maximizes neural responses, the iso-response paradigm which finds sets of stimuli giving rise to constant responses, and the system identification paradigm where the experimental goal is to estimate and possibly compare sensory processing models. We discuss various theoretical and practical aspects of adaptive firing rate optimization, including optimization with stimulus space constraints, firing rate adaptation, and possible network constraints on the optimal stimulus. We consider the problem of system identification, and show how accurate estimation of non-linear models can be highly dependent on the stimulus set used to probe the network. We suggest that optimizing stimuli for accurate model estimation may make it possible to successfully identify non-linear models which are otherwise intractable, and summarize several recent studies of this type. Finally, we present a two-stage stimulus design procedure which combines the dual goals of model estimation and model comparison and may be especially useful for system identification experiments where the appropriate model is unknown beforehand. We propose that fast, on-line stimulus optimization enabled by increasing computer power can make it practical to move sensory neuroscience away from a descriptive paradigm and toward a new paradigm of real-time model estimation and comparison.

Recently there have been significant developments in re-casting experiment design problems in system identification as convex optimization problems. The practical implementation of these methods is hampered by the fact that typically the in the optimization problem depend on the to be identified system. In this contribution we propose an adaptive certainty equivalence solution based on a recursively identified model. The input design is adapted by taking one Newton step using data from the last identified model.

The parameter estimation tuning is one of the procedures of system identification. One of the identification problems is to find an optimal model structure especially for representing the complex multivariable dynamic systems. Therefore, this problem needs to be solved by using multi-objective optimization with two objective functions namely minimum predictive error and model complexity. In this paper, the tuning of control parameters is studied before comparing multi-objective evolutionary algorithms. The framework is based on the system identification problems. In parameter tuning, two main qualitative parameters of evolutionary algorithms are focused on crossover rate and mutation rate. The multi-objective evolutionary algorithms used for this study are an elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective optimization using differential evolution (MOODE). The different parameter settings are compared in order to obtain good parameter setting for NSGA-II and MOODE. Then, the performance for both algorithms is also compared using Pareto front. The plotted graphs of two objective functions show the non-dominated fronts achieved by the algorithms. The results proved that MOODE shows an advantage in solving system identification problems in a multivariable nonlinear dynamic system.

System identification in the presence of nonlinear sensors

System identification in the presence of trends and outliers using sparse optimization

Synchronization of nonlinear dynamical systems with complex variables has attracted much more attention in various fields of science and engineering. In this paper, the problem of parameter identification and adaptive impulsive synchronization for a class of chaotic (hyperchaotic) complex nonlinear systems with uncertain parameters is investigated. Based on the theories of adaptive control and impulsive control, a synchronization scheme is designed to make a class of chaotic and hyperchaotic complex systems asymptotically synchronized, and uncertain parameters are identified simultaneously in the process of synchronization. Particularly, the proposed adaptive–impulsive control laws for synchronization are simple and can be readily applied in practical applications. The synchronization of two identical chaotic complex Chen systems and two identical hyperchaotic complex Lu systems are taken as two examples to verify the feasibility and effectiveness of the proposed controllers and identifiers.

SummaryThis contribution considers the problem of realizing an input signal with a desired autocorrelation sequence satisfying both input and output constraints for the system it is to be applied to. This is an important problem in system identification, firstly, because the quality and accuracy of the identified model are highly dependent on the excitation signal used during the experiment and secondly, because on real processes, it is often important to constrain the input and output of the process because of actuator saturation and safety considerations. The signal generation is formulated as a model predictive controller with probabilistic constraints to make the algorithm robust to model uncertainties and process noise. The corresponding optimization problem is then solved with tools from scenario‐based stochastic optimization. To reduce the model uncertainties, the method is made adaptive where a new model of the system and its uncertainties are reidentified. The algorithm is successfully applied to a simulation example and in a practical experiment for the identification of a quadruple tank lab process. Copyright © 2015 John Wiley & Sons, Ltd.

An adjoint sensitivity based approach to determine the gradient and Hessian of cost functions for system identification is presented. The motivation is the development of a computationally efficient approach relative to the direct differentiation technique and which overcomes the challenges of the step size selection in finite difference approaches. The discrete time measurements result in discontinuities in the Lagrange multipliers. The proposed approach is illustrated on the Lorenz 63 model where part of the initial conditions and model parameters are estimated.

Dynamic regressor extension and mixing is a new technique for parameter estimation that has proven instrumental in the solution of several open problems in system identification and adaptive control. A key property of the estimator is that, for linear regression models, it guarantees monotonicity of each element of the parameter error vector that is a much stronger property than monotonicity of the vector norm, as ensured with classical gradient or least-squares estimators. On the other hand, the overall performance improvement of the estimator is strongly dependent on the suitable choice of certain operators that enter in the design. In this paper we investigate the impact of these operators on the convergence properties of the estimator in the context of identification of linear time-invariant systems. In particular, we give some guidelines for their selection to ensure convergence under the same (persistence of excitation) conditions as standard identification schemes.

Taylor series approach to system identification, analysis and optimal control

A novel simple approach is presented for solving small sample size problem in nonlinear dynamic system identification where only a very small number of measured input and output data points are available. The technique is built upon an orthogonal least squares algorithm and a new resampling method called output jittering method,. The proposed algorithm is applied to the model identification of bioethanol production and it shows that a robust and reliable model can be obtained with the new system identification approach.

This paper is concerned with a particular control-oriented system identification problem recently considered by several authors. This problem has been referred to as the problem of worst-case system identification in H∞ in the literature. The formulation of this problem is worst-case/deterministic in nature. The available apriori information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The available aposteriori information consists-of a finite number of noisy plant point frequency response samples. The objective is to identify the plant transfer function in H∞ using the available apriori and aposteriori information. In this paper we resolve several important open issues pertaining to this problem. First, a method is presented for developing confidence that the available apriori information is correct. This method requires the solution of a certain nondifferentiable convex programming problem. Second, an essentially optimal identification algorithm is given for this problem. This algorithm is (worst-case strongy) optimal to within a factor of two. Finally, new upper and lower bounds on the optimal identification error for this problem are derived and used to estimate the identification error associated with the algorithm presented here. Interestingly, the development of each of the results described above draws heavily upon the classical Nevanlinna-Pick optimal interpolation theory. As such, the results of this paper establish a clear link between the areas of system identification and optimal interpolation theory.

Joint identification of plant rational models and noise distribution functions using binary-valued observations

An Information-Theoretic Approach to System Identification with Applying Tsallis Entropy