Jan-Erik Strömberg

Neural trees-using neural nets in a tree classifier structure

The concept of tree classifiers is combined with the popular neural net structure. Instead of having one large neural net to capture all the regions in the feature space, the authors suggest the compromise of using small single-output nets at each tree node. This hybrid classifier is referred to as a neural tree. The performance of this classifier is evaluated on real data from a problem in speech recognition. When verified on this particular problem, it turns out that the classifier concept drastically reduces the computational complexity compared with conventional multilevel neural nets. It is also noted that these data make it possible to grow trees online from a continuous data stream.<<ETX>>

The conceptual side of mode switching

For continuous dynamic systems there are many powerful methods for modelling. However, when dealing with systems undergoing abrupt behavioural changes, i.e. mode switching systems, the picture suddenly is changed. We here claim that the reason for this is that mode switching traditionally is treated by mathematical and/or logical solutions only. That is, at the wrong level of abstraction. We present several arguments supporting this view, and finally present our solution to this problem: the ideal switch concept.<<ETX>>

Proving dynamic properties in an aerospace application

We give an exposition to an ongoing research effort in cooperation with aerospace industries in Sweden. We report on an application of formal verification techniques on a landing gear system. This system consists of actuating hydromechanic and electromechanic hardware, and of controlling software components. We emphasize the need for modelling techniques and languages covering the whole spectrum from informal engineering documents, to hybrid mathematical models. In this modelling process we give as much weight to the physical environment as to the controlling software. We show the application of two verification methods for proving safety and timeliness properties of the closed loop system; first, using the proof system of extended duration calculus, and second by symbolic model checking.

Switched bond graphs as front-end to formal verification of hybrid systems

Formal verification of safety and timing properties of engineering systems is only meaningful if based on models which are systematically derived. In this paper we report on our experience using switched bond graphs for the modelling of hardware components in hybrid systems. We present the basic ideas underlying bond graphs in general and switched bond graphs in particular. Switched bond graphs are tailored for the modelling of physical systems undergoing abrupt structural changes. Such abrupt changes appear frequently in plants closed by discrete controllers. We illustrate our approach by means of an aircraft landing gear system and prove safety and timeliness properties using the proof system of extended duration calculus.

From Physical Modelling to Compositional Models of Hybrid Systems

By a hybrid system we mean a discrete controller in interaction with a physical environment. This paper discusses methodologies for incorporating physically grounded models in representations of hybrid systems. To this end, we study a driver support system, an example which includes unmodelled inputs. We consider models at different levels of abstraction. First, we show that discrete models of the environment can be obtained from the continuous models without losing relevant information. We do this using an analysis of the continuous state space. Dynamic Transition Systems (DTS) are used for the modular modelling at this level of abstraction. Next, we consider models using Hybrid Transition Systems (HTS). This can be seen as a modular version of timed transition systems allowing both differential and algebraic equations in each mode. Finally, we comment on expressivity requirements on hybrid formalisms for modelling realistic physical systems.

Extraction of diagnostic rules using recursive partitioning systems: A comparison of two approaches

There are several empirical systems based on principles of learning from examples that can be used as a tool for decision support by medical experts in medicine. We are comparing two systems of this kind, one based on Quinlans ID3 algorithm, and the other based on Breimans CART (Classification And Regression Trees) algorithm. Both of these methods represent the extracted knowledge in form of binary tree structured diagnostic rules. In this paper we present the most important features of the two systems and discuss important differences between the two; all this in a uniform framework. We then study the implications these differences and similarities make when applied to clinical data. The empirical study includes two medical data sets: the first one concerning patients with highly selective vagotomy (HSV) for duodenal ulcer surgery, and the second one concerning patients with non-specified liver disease.

Comparability and usefulness of newer and classical data analysis techniques. Application in medical domain classification

In the present paper three different approaches to the classification of objects between several a priori known, distinct classes are compared. These are: rough sets, DISQUAL method as well as classification and regression trees (CART). A common set of medical data forms a basis for the comparison. AU the methods allow for a mixture of continuous and discrete attributes on input via discretization of continuous ones. The latter is done automatically in CART but should be given a priori in two others. Thus sensitivity on changes in discretization is also studied.

On recursive construction of trees as models of dynamical systems

An issue that is of importance for control applications is discussed: how to construct the trees online, i.e. recursively, as more and more data become available. A theorem regarding recursive tree-building is stated and proved, and implementation issues are considered.<<ETX>>

Modelling and verification of hybrid systems: A case study

The problem of correctness and timing of reactions of an agent in interaction with a physical environment is addressed. To this end, a method based on composition of separate models of the software and the environment is used. To use available methods within the field of software verification, discrete representations of the continuous components are described systematically. A nontrivial case study within the domain of road traffic is used to illustrate the derivation of discrete models without losing information relevant to the verification task. The different modeling stages involved are shown first within an untimed formalism, and then in a formalism incorporating quantitative time.<<ETX>>

FuzzyCAT-towards a mathematical analysis of fuzzy controllers

The aim of this paper is to show that, contrary to what is commonly believed, it is possible to get rather simple analytic expressions for a class of fuzzy controllers. The authors describe a Maple package called FuzzyCAT that supports analysis and simulation of fuzzy controllers. The restrictions made in the program concern the shape of the membership functions, the defuzzification methods available and the number of input and output variables.<<ETX>>