Sirish L. Shah

Optimal

This note studies the problem of optimal H2 filtering in networked control systems (NCSs) with multiple packet dropout. A new formulation is employed to model the multiple packet dropout case, where the random dropout rate is transformed into a stochastic parameter in the systems representation. By generalization of the H2-norm definition, new relations for the stochastic -norm of a linear discrete-time stochastic parameter system represented in the state-space form are derived. The stochastic H2-norm of the estimation error is used as a criterion for filter design in the NCS framework. A set of linear matrix inequalities (LMIs) is given to solve the corresponding filter design problem. A simulation example supports the theory.

{\cal H}_{2}

This paper studies the problem of optimal filtering of discrete-time systems with random sensor delay, multiple packet dropout and uncertain observation. The random sensor delay, multiple packet dropout or uncertainty in observation is transformed to a stochastic parameter in the system representation. A new formulation enables us to design an optimal filter for a system with multiple packet dropout in sensor data. Based on a stochastic definition of the -norm of a system with a stochastic parameter, new relations for stochastic -norm are derived. The stochastic -norm of the estimation error is used as a criterion for the filter design. The relations derived for the new norm definition are used to obtain a set of linear matrix inequalities (LMIs) to solve the filter design problems. Simulation examples show the effectiveness of the proposed method.

Filtering in Networked Control Systems With Multiple Packet Dropout

This paper is concerned with the estimation of a suitable explicit expression for the feedback controller-invariant term of the closed-loop MIMO process from routine operating data. The feedback controller-invariant or the minimum-variance term is subsequently used as a benchmark standard for the evaluation of control performance of MIMO processes. This new approach, towards control-loop performance analysis of closed-loop MIMO processes, is based on filtering and correlation (FCOR) analysis of the process output and filtered data. The FCOR algorithm is intuitively simple and computationally efficient. However, it does require a priori knowledge or estimation of the time-delay or interactor matrix of the MIMO process. The proposed algorithm is evaluated by application to simulated and industrial processes.

Optimal H2 filtering with random sensor delay, multiple packet dropout and uncertain observations

Higher-order statistical (HOS) techniques were first proposed over four decades ago. This paper is concerned with higher-order statistical analysis of closed-loop data for diagnosing the causes of poor control-loop performance. The main contributions of this work are to utilize HOS tools such as cumulants, bispectrum and bicoherence to develop two new indices: the non-Gaussianity index (NGI) and the nonlinearity index (NLI) for detecting and quantifying non-Gaussianity and nonlinearity that may be present in regulated systems, and to use routine operating data to diagnose the source of nonlinearity. The new indices together with some graphical plots have been found to be useful in diagnosing the causes of poor performance of control loops. Successful applications of the proposed method are demonstrated on simulated as well as industrial data. This study clearly shows that HOS-based methods are promising for closed-loop performance monitoring.

Good, bad or optimal? Performance assessment of multivariable processes

Outliers are observations that do not follow the statistical distribution of the bulk of the data, and consequently may lead to erroneous results with respect to statistical analysis. Many conventional outlier detection tools are based on the assumption that the data is identically and independently distributed. In this paper, an outlier-resistant data filter-cleaner is proposed. The proposed data filter-cleaner includes an on-li ne outlier-resistant estimate of the process model and combines it with a modified Kalman filter to detect and “clean” outliers. The advantage over existing methods is that the proposed method has the following features: (a) a priori knowledge of the process model is not required; (b) it is applicable to autocorrelated data; (c) it can be implemented on-line; and (d) it tries to only clean (i.e., detects and replaces) outliers and preserves all other information in the data.

Diagnosis of poor control-loop performance using higher-order statistics

Metabolomics is an emerging field providing insight into physiological processes. It is an effective tool to investigate disease diagnosis or conduct toxicological studies by observing changes in metabolite concentrations in various biofluids. Multivariate statistical analysis is generally employed with nuclear magnetic resonance (NMR) or mass spectrometry (MS) data to determine differences between groups (for instance diseased vs healthy). Characteristic predictive models may be built based on a set of training data, and these models are subsequently used to predict whether new test data falls under a specific class. In this study, metabolomic data is obtained by doing a (1)H NMR spectroscopy on urine samples obtained from healthy subjects (male and female) and patients suffering from Streptococcus pneumoniae. We compare the performance of traditional PLS-DA multivariate analysis to support vector machines (SVMs), a technique widely used in genome studies on two case studies: (1) a case where nearly complete distinction may be seen (healthy versus pneumonia) and (2) a case where distinction is more ambiguous (male versus female). We show that SVMs are superior to PLS-DA in both cases in terms of predictive accuracy with the least number of features. With fewer number of features, SVMs are able to give better predictive model when compared to that of PLS-DA.

On-line outlier detection and data cleaning

Abstract This paper studies the problem of H ∞ filtering in networked control systems (NCSs) with multiple packet dropouts. A new formulation enables us to assign separate dropout rates from the sensors to the controller and from the controller to the actuators. By employing the new formulation, random dropout rates are transformed into stochastic parameters in the system’s representation. A generalized H ∞ -norm for systems with stochastic parameters and both stochastic and deterministic inputs is derived. The stochastic H ∞ -norm of the filtering error is used as a criterion for filter design in the NCS framework. A set of linear matrix inequalities (LMIs) is given to solve the corresponding filter design problem. A simulation example supports the theory.

Analysis of Metabolomic Data Using Support Vector Machines

For a multirate sampled-data system consisting of a continuous-time process with or without a time delay, a sampler with period nT and a zero-order hold with period mT (m < n), we study the problem of identifying a fast single-rate model with sampling period mT based on multirate input-output data. This problem is solved in two steps: First, we identify a lifted state-space model for the multirate system by extending existing subspace identification algorithms to take into account the causality constraint in the lifted model; next, based on the lifted model, we extract a state-space model for the fast single-rate system. Such fast-rate models are useful for many applications such as inferential control. Other related topics discussed in the paper include observability of lifted models in the presence of time delay and time-delay estimation from multirate data. Finally, we apply and test the proposed algorithms to an experimental setup involving a continuously stirred tank heater.

Optimal H∞ filtering in networked control systems with multiple packet dropouts

Abstract This article describes principal component analysis (PCA) of the power spectra of data from chemical processes. Spectral PCA can be applied to the measurements from a whole unit or plant because spectra are invariant to the phase lags caused by time delays and process dynamics. The same comment applies to PCA using autocovariance functions, which was also studied. Two case studies are presented. One was derived from simulation of a pulp process. The second was from a refinery involving 37 tags. In both cases, PCA clusters were observed which were characterised by distinct spectral features. Spectral PCA was compared with PCA using autocovariance functions. The performance was similar, and both offered an improvement over PCA using the time domain signals even when time shifting was used to align the phases.

Identification of fast-rate models from multirate data

Abstract In this paper, we study digital control systems with non-uniform updating and sampling patterns, which include multirate sampled-data systems as special cases. We derive lifted models in the state-space domain. The main obstacle for generalized predictive control (GPC) design using the lifted models is the so-called causality constraint. Taking into account this design constraint, we propose a new GPC algorithm, which results in optimal causal control laws for the non-uniformly sampled systems. The solution applies immediately to multirate sampled-data systems where rates are integer multiples of some base period.