Aleksandar Lj. Juloski

Identification of Hybrid Systems A Tutorial

This tutorial paper is concerned with the identification of hybrid models, i.e. dynamical models whose behavior is determined by interacting continuous and discrete dynamics. Methods specifically aimed at the identification of models with a hybrid structure are of very recent date. After discussing the main issues and difficulties connected with hybrid system identification, and giving an overview of the related literature, this paper focuses on four different approaches for the identification of switched affine and piecewise affine models, namely an algebraic procedure, a Bayesian procedure, a clustering-based procedure, and a bounded-error procedure. The main features of the selected procedures are presented, and possible interactions to still enhance their effectiveness are suggested.

A Bayesian approach to identification of hybrid systems

In this paper, we present a novel procedure for the identification of hybrid systems in the class of piecewise ARX systems. The presented method facilitates the use of available a priori knowledge on the system to be identified, but can also be used as a black-box method. We treat the unknown parameters as random variables, described by their probability density functions. The identification problem is posed as the problem of computing the a posteriori probability density function of the model parameters, and subsequently relaxed until a practically implementable method is obtained. A particle filtering method is used for a numerical implementation of the proposed procedure. A modified version of the multicategory robust linear programming classification procedure, which uses the information derived in the previous steps of the identification algorithm, is used for estimating the partition of the piecewise ARX map. The proposed procedure is applied for the identification of a component placement process in pick-and-place machines.

Comparison of four procedures for the identification of hybrid systems

In this paper we compare four recently proposed procedures for the identification of PieceWise AutoRegressive eXogenous (PWARX) and switched ARX models. We consider the clustering-based procedure, the bounded-error procedure, and the Bayesian procedure which all identify PWARX models. We also study the algebraic procedure, which identifies switched linear models. We introduce quantitative measures for assessing the quality of the obtained models. Specific behaviors of the procedures are pointed out, using suitably constructed one dimensional examples. The methods are also applied to the experimental identification of the electronic component placement process in pick-and-place machines.

Observer Designs for Experimental Non-Smooth and Discontinuous Systems

This brief presents the design and implementation of observer design strategies for experimental non-smooth continuous and discontinuous systems. First, a piece-wise linear observer is implemented for an experimental setup consisting of a harmonically excited flexible steel beam with a one-sided support which can be considered as a benchmark for a class of flexible mechanical systems with one-sided restoring characteristics. Second, an observer is developed for an experimental setup that describes a dynamic rotor system which is a benchmark for motion systems with friction and flexibility. In both cases, the implemented observers guarantee global asymptotic stability of the estimation error dynamic in theory. Simulation and experimental results are presented to demonstrate the performance of the observers in practice. These results support the use of (switched) observers to achieve state reconstruction for such non-smooth and discontinuous mechanical systems.

On the equivalence of switched affine models and switched ARX models

This paper proves the formal equivalence between the class of switched affine systems and the class of switched autoregressive systems with exogenous inputs. These classes of hybrid dynamical systems have been studied recently for various purposes. It is shown that any observable switched affine system admits a representation as a switched autoregressive system and every switched autoregressive system admits a representation as a switched affine system

Recent techniques for the identification of piecewise affine and hybrid systems

The problem of piecewise affine identification is addressed by studying four recently proposed techniques for the identification of PWARX/HHARX models, namely a Bayesian procedure, a bounded-error procedure, a clustering-based procedure and a mixed-integer programming procedure. The four techniques are compared on suitably defined one-dimensional examples, which help to highlight the features of the different approaches with respect to classification, noise and tuning parameters. The procedures are also tested on the experimental identification of the electronic component placement process in pick-and-place machines.

A Multi Target Track Before Detect Application

This paper deals with a radar track before detect application in a multi target setting. Track before detect is a method to track weak objects (targets) on the basis raw radar measurements, e.g. the reflected target power. In classical target tracking, the tracking process is performed on the basis of pre-processed measurements, that are constructed from the original measurement data every time step. In this way no integration over time takes place and information is lost. In this paper we will give a modelling setup and a particle filter based algorithm to deal with a multiple target track before detect situation. In simulations we show that, using this method, it is possible to track multiple, closely spaced, (weak) targets.

Control of quantized linear systems: an l/sub 1/-optimal control approach

In many practical situations, the outputs of a plant are not measured exactly, but are corrupted by quantization errors. Often the effect of the quantization error is neglected in the control design phase, which can lead to undesirable effects like limit cycles and even chaotic behavior once the controller has been implemented. In this paper we present a method based on l/sub 1/ optimal control that minimizes the amplitude of the oscillations in the to-be-controlled variables. Analytical and numerical examples illustrate the elegance of the l/sub 1/-theory in this setting.

Comparison of three procedures for the identification of hybrid systems

In This work, three recently proposed procedures for the identification of piece-wise autoregressive exogenous (PWARX) models are compared. Quantitative measures for the quality of the obtained models are proposed. Using one dimensional examples, specific behaviors of the methods are pointed out. An experimental example is considered as well.

Switched and piecewise affine systems

Book abstract: Setting out core theory and reviewing a range of new methods, theoretical problems and applications, this handbook shows how hybrid dynamical systems can be modelled and understood. 60 expert authors involved in the recent research activities and industrial application studies provide practical insights on topics ranging from the theoretical investigations over computer-aided design to applications in energy management and the process industry. Structured into three parts, the book opens with a thorough introduction to hybrid systems theory, illustrating new dynamical phenomena through numerous examples. Part II then provides a survey of key tools and tool integration activities. Finally, Part III is dedicated to applications, implementation issues and system integration, considering different domains such as industrial control, automotive systems and digital networks. Three running examples are referred to throughout the book, together with numerous illustrations, helping both researchers and industry professionals to understand complex theory, recognise problems and find appropriate solutions.