Class Of Identification Algorithms Research Articles

Regularized Local Basis Function Approach to Identification of Nonstationary Processes

The problem of identification of nonstationary stochastic processes (systems or signals) is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed regularized local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide a sequence of point estimates corresponding to consecutive instants of time. Based on the results of theoretical analysis, the paper addresses and solves all major problems associated with implementation of the new class of estimators, such as optimization of the regularization matrix, adaptive selection of the number of basis functions and the width of the local analysis interval, and reduction of complexity of the computational algorithms.

Generalized Savitzky–Golay filters for identification of nonstationary systems

The problem of identification of nonstationary systems using noncausal estimation schemes is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide a sequence of point estimates corresponding to consecutive instants of time. Based on the results of theoretical analysis conducted for nonstationary finite impulse response systems the paper proposes two mechanisms for adaptive selection of the number of basis functions and the size of the local analysis window.

System Identification of Just Walk: Using Matchable-Observable Linear Parametrizations

System identification approaches have been used to design an experiment, generate data, and estimate dynamical system models for Just Walk, a behavioral intervention intended to increase physical activity in sedentary adults. The estimated models serve a number of important purposes, such as understanding the factors that influence behavior and as the basis for using control systems as decision algorithms in optimized interventions. A class of identification algorithms known as matchable-observable linear identification has been reformulated and adapted to estimate linear time-invariant models from data obtained from this intervention. The experimental design, estimation algorithms, and validation procedures are described, with the best models estimated from data corresponding to an individual intervention participant. The results provide insights into the individual and the intervention, which can be used to improve the design of future studies.

Functional identification of an antennal lobe DM4 projection neuron of the fruit fly

A rich set of genetic tools and extensive anatomical data make the olfactory system of the fruit fly a neural circuit of choice for studying function in sensory systems. Though a substantial amount of work has been published on the neural coding of olfactory sensory neurons (OSNs) of the fruit fly, yet little is known how projection neurons (PNs) encode time-varying odor stimuli [1]. Here we address this question with in vivo experiments coupled with a phenomenological characterization of the spiking activity of PNs. Recently, a new class of identification algorithms called Channel Identification Machines (CIMs) [2] was proposed for identifying dendritic processing in simple neural circuits using conditional phase response curves (cPRCs) [3]. By combining cPRCs with the reduced project-integrated-andfire neuron (PIF) model [4], the CIM algorithms identify a complete phenomenological description of spike generation of a biological neuron for weak to moderately strong stimuli. Moreover, the identification method employed does not require white noise stimuli nor an infinitesimal pulse injection protocol as widely used in the past [5]. Here we identify the PNs both in silico and in vivo. Starting with simulations, we investigate the feasibility of the CIM method on PNs modeled as pseudo uni-polar neurons in silico, as shown in Figures 1.(B) and 1.(C). We then systematically convert the CIM method into a stepby-step experimental protocol, and carry it out in vivo by injecting currents into PNs using the patch clamping technique [6,7]. A snapshot of PN patching is depicted in Figure 1.(A).

The asymptotic variance of the PBSIDopt algorithm

It is well-known that system identification is a valuable technique to obtain compact models for controller design and prediction. Subspace identification methods are of interest since they solely rely on tools from linear algebra and their ability to directly work with data generated by systems with multiple inputs and outputs. With respect to other methods (e.g. Prediction Error (PE)), subspace methods do not have straightforward asymptotic variance expressions. However, recently some papers appeared with asymptotic variance expressions for a certain class of identification algorithms that merge ideas from PE and subspace methods. In this paper we derive the asymptotic variance expression for the PBSIDopt algorithm and derive manageable expressions under some reasonable assumptions. We conclude the paper with two simulation examples where we show the strength of the proposed method.

Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part II: Algorithms and Performance Analysis12

The present work proposes a new class of algorithms for identification of fast linear time-varying systems on short time intervals, based on the biorthogonal function decomposition. When certain features of the system dynamics are known a priori, the algorithms admit their embedding into the identification procedure through the choice of the matching bases, yielding the rapidly convergent identification laws. The speed-up is attained via utilizing both time and frequency localized bases, permitting identification of fewer coefficients without noticeable loss of accuracy. Simulation shows that the resulting high speed identification algorithms can reject small persistent random disturbances as well as capture the fast changes in system dynamics. The algorithm development is based on the results of Part I where it is shown that the sets of all bounded-input-bounded-output (BIBO) stable or l2-stable linear discrete-time-varying (LTV) systems are Banach spaces, and modeling and identification of these systems are reducible to linear approximation problems in a Banach space setting.

Guaranteed stability with subspace methods

We show how stability of models can be guaranteed when using the class of identification algorithms which have become known as ‘subspace methods’. In many of these methods the ‘ A’ matrix is obtained (or can be obtained) as the product of a shifted matrix with a pseudo-inverse. We show that whenever the shifted matrix is formed by introducing one block of zeros in the appropriate position, then a stable model results. The cost of this is some (possibly large) distortion of the results, but in some applications that is outweighed by the advantage of guaranteed stability.

Identification and Control Algorithm for Bilinear Delta Operator Systems

A class of identification algorithms and a controller based on pole assignment are derived for stochastic bilinear delta operator systems. Stability and convergence results are then derived under reasonable assumptions on the system for the adaptive algorithms obtained by combining the identification and control algorithms. The algorithms presented here are the first for delta operator representations of stochastic bilinear systems.

A class of algorithms for identification in H/sub infinity /: continuous-time case

The problem of system identification in H/sub infinity / for the continuous-time case is investigated. It is shown that the class of systems with a lower bound on the relative stability, an upper bound on the steady-state gain, and an upper bound on the roll-off rate is admissible. This allows one to develop a class of robustly convergent nonlinear algorithms. The algorithms in this class have a two-stage structure and are characterized by the use of window functions. Explicit worst-case error bounds in H/sub infinity / norm between the identified model and the unknown system are given for a particular algorithm. An example is provided to illustrate the application of the results obtained. >