Duality, observability, and controllability for linear time-varying descriptor systems

A characterization of observability for linear time-varying descriptor systemsE(t)x(t)+F(t)x(t)=B(t)u(t), y(t)=C(t)x(t) was recently developed. NeitherE norC were required to have constant rank. This paper defines a dual system, and a type of controllability so that observability of the original system is equivalent to controllability of the dual system. Criteria for observability and controllability are given in terms of arrays of derivatives of the original coefficients. In addition, the duality results of this paper lead to an improvement on a previous fundamental structure result for solvable systems of the formE(t)x(t)+F(t)x(t)=f(tt).

Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

Genetic least squares for system identification

The recursive least-squares algorithm with a forgetting factor has been extensively applied and studied for the on-line parameter estimation of linear dynamic systems. This paper explores the use of genetic algorithms to improve the performance of the recursive least-squares algorithm in the parameter estimation of time-varying systems. Simulation results show that the hybrid recursive algorithm (GARLS), combining recursive least-squares with genetic algorithms, can achieve better results than the standard recursive least-squares algorithm using only a forgetting factor.

Performance analysis of near-far resistant CDMA detectors-influence of system parameter estimation errors

Little has been reported on the performance of near-far resistant CDMA detectors in the presence of system parameter estimation errors (SPEEs). Starting with the general mathematical model of matched filters, the paper examines the effects of three classes of SPEEs, i.e., time-delay, carrier phase, and carrier frequency errors, on the performance (BER) of an emerging type of near-far resistant coherent DS/SSMA detector, i.e., the linear decorrelating detector. For comparison, the corresponding results for the conventional detector are also presented. It is shown that the linear decorrelating detector can still maintain a considerable performance advantage over the conventional detector even when some SPEEs exist.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Time-varying coefficients in the almost ideal demand system: An empirical appraisal

This paper provides a generalisation of the structural time series version of the Almost Ideal Demand System (AIDS) that allows for time-varying coefficients (TVC/AIDS) in the presence of cross-equation constraints. An empirical appraisal of the TVC/AIDS is made using a dynamic AIDS with trending intercept as the baseline model with a data set from the Italian Household Budget Survey (1986-2001). The assessment is based on four criteria: adherence to theoretical constraints, statistical diagnostics on residuals, forecasting performance and economic meaningfulness. No clear evidence is found for superior performance of the TVC/AIDS, apart from improved short-term forecasts.

Extraction behavior of the synergistic system 2,6-bis-(benzoxazolyl)-4-dodecyloxylpyridine and 2-bromodecanoic acid using Am and Eu as radioactive tracers

In this study, the extraction properties of a synergistic system consisting of 2,6-bis-(benzoxazolyl)-4-dodecyloxylpyridine (BODO) and 2-bromodecanoic acid (HA) in tert-butyl benzene (TBB) have been investigated as a function of ionic strength by varying the nitrate ion and perchlorate ion concentrations. The influence of the hydrogen ion concentration has also been investigated. Distribution ratios between 0.03-12 and 0.003-0.8 have been found for Am(III) and Eu(HI), respectively, but there were no attempts to maximize these values. It has been shown that the distribution ratios decrease with increasing amounts of ClO4-, NO3-, and H+. The mechanisms, however, by which the decrease occurs, are different. In the case of increasing perchlorate ion concentration, the decrease in extraction is linear in a log-log plot of the distribution ratio vs. the ionic strength, while in the nitrate case the complexation between nitrate and Am or Eu increases at high nitrate ion concentrations and thereby decreases the distribution ratio in a non-linearway. The decrease in extraction could be caused by changes in activity coefficients that can be explained with specific ion interaction theory (SIT); shielding of the metal ions, and by nitrate complexation with Am and Eu as competing mechanism at high ionic strengths. The separation factor between Am and Eu reaches a maximum at similar to1 M nitrate ion concentration. Thereafter the values decrease with increasing nitrate ion concentrations.

Structure adaptation of linear MMSE adaptive filters

The tap-length, or the number of the taps, is an important structural parameter of the linear MMSE adaptive filter. Although the optimum tap-length that balances performance and complexity varies with scenarios, most current adaptive filters fix the tap-length at some compromise value, making them inefficient to implement especially in time-varying scenarios. A novel gradient search based variable tap-length algorithm is proposed, using the concept of the pseudo-fractional tap-length, and it is shown that the new algorithm can converge to the optimum tap-length in the mean. Results of computer simulations are also provided to verify the analysis.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

Conditioning of incremental variational data assimilation, with application to the Met Office system

Implementations of incremental variational data assimilation require the iterative minimization of a series of linear least-squares cost functions. The accuracy and speed with which these linear minimization problems can be solved is determined by the condition number of the Hessian of the problem. In this study, we examine how different components of the assimilation system influence this condition number. Theoretical bounds on the condition number for a single parameter system are presented and used to predict how the condition number is affected by the observation distribution and accuracy and by the specified lengthscales in the background error covariance matrix. The theoretical results are verified in the Met Office variational data assimilation system, using both pseudo-observations and real data.

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.