Qualitative simulation predicts the set of possible behaviors...

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In this paper we want to describe some examples of the active interaction that takes place at the border of rational approximation theory and linear system theory. These examples are mainly taken from the period 1950-1999 and are described only at a skindeep level in the simplest possible (scalar) case. We give comments on generalizations of these problems and how they opened up new ranges of research that after a while lived their own lives. We also describe some open problems and future work that will probably continue for some years after 2000. Key words: Rational approximation, linear system theory, model reduction, identication. ? This work is partially supported by the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Minister's OÆce for Science, Technology and Culture. The scientic responsibility rests with the authors. 1 This work of this author is also partially supported by the Fund for Scientic Research (FWO), project \Orth...

The purpose of this paper is to marry the two concepts of Multiple Model Adaptive Control and Safe Adaptive Control. In its simplest form, Multiple Model Adaptive Control involves a supervisor switching among one of a finite number of controllers as more is learnt about the plant, until one of the controllers is finally selected and remains unchanged. Safe Adaptive Control is concerned with ensuring that when the controller is changed in an adaptive control algorithm, the frozen plant-controller combination is never (closed loop) unstable. This is a nontrivial task since by definition of an adaptive control problem, the plant is not fully known. The proposed solution method involves a frequency-dependent performance measure and employs the Vinnicombe metric. The resulting safe switching guarantees depend on the extent to which a closed loop transfer function can be accurately identified.

A model is proposed to assist software test managers in controlling the behavior and progress of the Software Test Process (STP) by allowing them to compare predicted behavior against observed progress made at various checkpoints. The model, whose parameters are based on measured data and process characteristics, generates the predicted behavior. An algorithm for the parameter estimation is set forth. The error between the predicted and desired behavior is used to drive a parametric control algorithm that tells the manager how to correct for schedule deviations.

In this paper, we consider linear systems in input-output form and introduce a new adaptive linear quadratic Gaussian (LQG) control scheme which is shown to be self-optimizing. The identification algorithms incorporates a cost-biasing term, which favors the parameters with smaller LQG optimal cost and a second term that aims at moderating the time-variability of the estimate. The corresponding closed-loop scheme is proven to be stable and to achieve an asymptotic LQG cost equal to the one obtained under complete knowledge of the true system (self-optimization). The results of this paper extend in a non trivial way previous results established along the cost-biased approach in other settings.

Many model based solutions to diagnosis problems in SIengines have been discussed in literature. However most presented methods are useful only for a specific class of faults. Here a systematic and more general method is presented. With this method, which is based on a structure of hypothesis tests, it is possible to diagnose a large variety of different types of faults. The method is applied to the diagnosis of sensor-faults and leakage in the air-intake system of an SI-engine. The features of the method are demonstrated by using experiments on a real SI-engine. The experiments show that the method is capable to diagnose both leakage and different types of sensor faults. Both detection and isolation are considered. It is for example possible to distinguish between a manifold leak and a manifold pressure sensor fault.

Support vector machines have been very successful in pattern recognition and function estimation problems. In this paper we introduce the use of least squares support vector machines (LS-SVM's) for the optimal control of nonlinear systems. Linear and neural full static state feedback controllers are considered. The problem is formulated in such a way that it incorporates the N-stage optimal control problem as well as a least squares support vector machine approach for mapping the state space into the action space. The solution is characterized by a set of nonlinear equations. An alternative formulation as a constrained nonlinear optimization problem in less unknowns is given, together with a method for imposing local stability in the LSSVM control scheme. The results are discussed for support vector machines with radial basis function kernel. Advantages of LS-SVM control are that no number of hidden units has to be determined for the controller and that no centers have to be specied for the Gaussian kernels when applying Mercer's condition. The curse of dimensionality is avoided in comparison with dening a regular grid for the centers in classical radial basis function networks. This is at the expense of taking the trajectory of state variables as additional unknowns in the optimization problem, while classical neural network approaches typically lead to parametric optimization problems. In the SVM methodology the number of unknowns equals the number of training data, while in the primal space the number of unknowns can be innite dimensional. The method is illustrated both on stabilization and tracking problems including examples on swinging up an inverted pendulum with local stabilization at the endpoint and a tracking problem for a ball and beam system. Keywords. N...

A novel approach to modeling the software development process is presented. This approach is based on the use of concepts and techniques from the theory of state variables and feedback control. The reasons to use this approach and its advantages are presented. A model for the Software Test Process is developed to show the approach applicability to the software development process. The assumptions and choice of parameters used in the model are discussed.

This paper proposes the use of variational Kalman ltering as an inference technique for adaptive classi cation in a brain computer interface (BCI). The proposed algorithm translates EEG segments adaptively into probabilities of cognitive states. It thus allows for non-stationarities in the joint process over cognitive state and generated EEG which may occur during a consecutive number of trials. Nonstationarities may have technical reasons (e.g. changes in impedance between scalp and electrodes) or be caused by learning eects in subjects. We compare the performance of the proposed method against an equivalent static classi er by estimating the generalization accuracy and the bit rate of the BCI. Using data from two studies with healthy subjects, we conclude that adaptive classi cation signi cantly improves BCI performance. Averaging over all subjects that participated in the respective study, we obtain, depending on the cognitive task pairing, an increase both in generalization accuracy and bit rate of up to 8%. We may thus conclude that adaptive inference can play a signi cant contribution in the quest of increasing bit rates and robustness of current BCI technology. This is especially true since the proposed algorithm can be applied in real time.