Reduction of the number of variables in data from a so-called electronic tongue contributes to simpler model calculations and less storage requirements. In this study, we have developed a model for this purpose. This model describes the response from the electrodes in the electronic tongue with two exponential functions plus a constant term, i(t) = k + kf e-ta + kc e-tß, where t is the time. From the model, five parameters which describe the signal are extracted. These parameters can be used as inputs instead of the original signal to any multivariate algorithm. The results show that the variables obtained are at least as good as the original data to separate between different classes, even though the number of parameters has been reduced between 80 and 199 times. © 2002 Elsevier Science B.V. All rights reserved.
In this paper, three data compression methods are investigated to determine their ability to reduce large data sets obtained by a voltammetric electronic tongue without loss of information, since compressed data sets will save data storage and computational time. The electronic tongue is based on a combination of non-specific sensors and pattern recognition tools, such as principal component analysis (PCA). A series of potential pulses of decreasing amplitude are applied to one working electrode at a time and resulting current transients are collected at each potential step. Voltammograms containing up to 8000 variables are subsequently obtained. The methods investigated are wavelet transformation (WT) and hierarchical principal component analysis (HPCA). Also, a new chemical/physical model based on voltammetric theory is developed in order to extract interesting features of the current transients, revealing different information about species in solutions. Two model experiments are performed, one containing solutions of different electroactive compounds and the other containing complex samples, such as juices from fruits and tomatoes. It is shown that WT and HPCA compress the data sets without loss of information, and the chemical/physical model improves the separations slightly. HPCA is able to compress the two data sets to the largest extent, from 8000 to 16 variables. When data sets are scaled to unit variance, the separation ability improves even further for HPCA and the chemical/physical model. © 2001 Elsevier Science B.V.
We investigate how to tune the thermostat hysteresis for a system of interconnected thermal processes. Using linear programming techniques and the worst-case analysis we compute switch levels for the controller to make the system stay close to the desired temperature levels. Both the cases with and without amplitude bounded disturbances are treated. The same technique can also be applied to a system of interconnected tanks despite the fact that such a system is nonlinear.
In this note we investigate how to tune the thermostat hysteresis for a system of interconnected thermal processes. Using linear programming techniques and worst-case analysis we compute switch levels for the controller to make the system stay close to desired temperature levels. Both the case with and without amplitude bounded disturbances are treated. The same technique can also be applied to a system of interconnected tanks despite the fact that such a system is nonlinear.
In recent years, the advent of efficient methods for solving linear matrix inequality (LMI) problems has yielded a new interesting class of Lyapunov functions, the piecewise quadratic Lyapunov functions, subject to efficient computation. This class has shown promise, e.g. in the stability analysis of hybrid systems. In this paper, we describe one example that we have analyzed in order to investigate how LMI methods and piecewise quadratic Lyapunov functions can be used to iteratively synthesize a switched control law in order to obtain an improved decay rate. The example shows that piecewise quadratic Lyapunov functions are not sufficient to analyze the decay rate of a piecewise affine system, given that the partitioning used in the Lyapunov function is the same as in the piecewise affine system. As noted in other performance analysis examples, a finer partitioning is needed
The paper deals with the stabilizability and passifiability properties of a class of hybrid dynamical systems. The systems under consideration are composed of a continuous time invariant plant and discrete event controller. An algebraic criterion for existence of a Lyapunov function for a piecewise linear system is given. Based on these results some passifiability issues are considered.
A linear feature extraction technique for asymmetric distributions is introduced, the asymmetric class projection (ACP). By emph {asymmetric classification} is understood discrimination among distributions with different covariance matrices. Two distributions with unequal covariance matrices do not in general have a symmetry plane, a fact that makes the analysis more difficult compared to the symmetric case. The ACP is similar to linear discriminant analysis (LDA) in the respect that both aim at extracting discriminating features (linear combinations or projections) from many variables. However, the drawback of the well known LDA is the assumption of symmetric classes with separated centroids. The ACP, incontrast, works on (two) possibly concentric distributions with unequal covariance matrices. The ACP is tested on data from anarray of semiconductor gas sensors with the purpose of distinguish bad grain from good.
A linear feature extraction technique for asymmetric distributions is introduced, the asymmetric class projection (ACP). By asymmetric classification is understood discrimination among distributions with different covariance matrices. Two distributions with unequal covariance matrices do not in general have a symmetry plane, a fact that makes the analysis more difficult compared to the symmetric case. The ACP is similar to linear discriminant analysis (LDA) in the respect that both aim at extracting discriminating features (linear combinations or projections) from many variables. However, the drawback of the well known LDA is the assumption of symmetric classes with separated centroids. The ACP, incontrast, works on (two) possibly concentric distributions with unequal covariance matrices. The ACP is tested on data from anarray of semiconductor gas sensors with the purpose of distinguish bad grain from good.
A common problem in industry is the issue of safety controllers. Usually there is a basic controller that works well for normal conditions, but when certain state variables get too large we need to switch to a safety controller in order to get the state back to a normal level. The design of the safety controller such that it works well together with the basic controller is the topic of the paper. In practice, the design is often done in an ad hoc manner. The paper describes an approach to extending a given static output feedback control law with a safety controller. The safety controller is activated when the state gets close to the forbidden region in state space. It pushes the state to a safe distance from the forbidden region within a maximum prescribed time despite disturbances. It does this with a prescribed bound on the input and in a manner that guarantees stability of the overall system. The switching between the two controllers takes place through hysteresis, this helps to avoid chattering. The method is based on LMIs which ensures scalability to large systems. However, the LMI approach imposes some conservatism on the results. Also, the method is as at present limited to systems with a relative degree one from the input to a specific output of the system
A new method to optimize with orthonormal constraints is described, where a particular composition of plane (Givens) rotations is used to parameterize decision variables in terms of angles. It is showed that this parameterization is complete and that any orthonormal k-by-nmatrix can be derived to a set of no more than kn-k(k+1) angles. The technique is applied to the emph {feature extraction problem} where a linear subspace is optimized with respect to non-linear objective functions. The Optimal Discriminative Projection (ODP) algorithm is described. ODP is a data compression or feature extraction algorithm that combines powerful model optimization with regularization to avoid over training. The ODP is used primarily for classification problems.