Date of final exam: 11/02/1999

E-mail: maroni@elet.polimi.it

Tutor: Prof.  P. Bolzern, Politecnico di Milano

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H-infinity filtering and prediction techniques   ___________________________________________________________________________________________________________

Advisor:

Prof.  P. Bolzern, Politecnico di Milano

Summary of the thesis

H-infinity filtering techniques are widely adopted when either no a priori information on the disturbance statistics is available or the designer aims to cope with the worst noise perturbation according to some criterion.
The objective of these techniques is to design a filter that minimizes the maximum of the estimation error energy with respect to any admissible disturbance. Actually, a suboptimal problem is often solved in which the ratio of the estimation error to the noise energy is bounded by a prescribed level of attenuation.
Given a dynamic system, the H-infinity estimation problem consists of estimating a linear combination of the state vector by exploiting the knowledge of the measurable system variables.
In the literature, two different problems have been treated: in the finite-horizon (FH) context, the designer is interested in the behavior of the estimated variables along a given fixed time interval, whereas in the infinite-horizon (IH) problem, all the positive time instants are taken into account.
A first issue addressed in the present work is the study of the FH filter as the horizon width tends to infinity. Actually, it is not sure that such a filter converges to the IH one. Moreover, unlike the standard Kalman filter, it is possible that, for some value of the final time, the FH filter does not exist any more. In this thesis, a new technique for analyzing the described issue has been developed and a sufficient condition for convergence has been worked out. The same approach has been applied to the problem of filtering, one-step ahead prediction, multi-step ahead prediction and, with some variations, to the sampled-data problem.
The second issue addressed in this dissertation concerns the study of IH multi-step prediction and smoothing problems via the so-called J-spectral factorization approach. Such a methodology extends the intuitive notion of signal spectrum to deal with H-infinity problems. In order to do that, a vector space associated with a possibly negative norm, is defined. By exploiting existing results on filtering, we propose a method for deriving J-spectral factors for prediction and smoothing. Doing so, these problems can be solved without requiring any augmentation of the size of the system.
Finally, the problem of singular filtering is treated. Starting from the concept of Interactor Matrix and exploiting the available results in singular Kalman filtering, we introduce the definition of J-Spectral Interactor Matrix. Such a matrix is capable of getting rid of the system delays and, in turn, of transforming the singular problem into a regular one that can be solved by means of standard techniques. In this context, we are also able to split the solution into two parts, the first one related to the nonminimum phase finite zeros of the original system and the second one associated with the system delays.
 
 

MINORS

Deadlock avoidance control for manufacturing systems with multiple capacity resources

Advisor: Prof. L. Ferrarini, Dipartimento di Elettronica e Informazione, Politecnico di Milano

The subject of this research is a manufacturing system model introduced by Banaszak, Krogh and by Tamaki, Araki. Such a model is based on Petri nets and it is constituted by many interacting modules. Each of these modules represents a different process flow necessary to the realization of a product. The interaction between modules is given by the use of resources (work station, transport bus, etc) shared by two or more process flows. The problem of deadlock avoidance arises when there exists a set of resources that are allocated to operations that cannot release them. The objective of this work is that of finding control policies such that the system cannot reach the deadlock configuration described above. The solution to this problem strongly exploits the particular structure of the Petri net associated with manufacturing systems.
 

Tyre parameters identification for the study of vehicle lateral dynamics

Advisor: Prof. S. Bittanti, Dipartimento di Elettronica e Informazione, Politecnico di Milano

Vehicle handling is one of the most important features in the design of both new cars and new tyres. In this work we develop a complete nonlinear model of the vehicle lateral dynamics, including the load transfer behaviour. Then, by using standard estimation techniques based on an extended Kalman filter we estimate the tyre parameters associated with the well-known model due to Pacejika. Finally, a simulator has been developed in order both to validate the results obtained in the estimation phase and to provide a way for predicting the vehicle behaviour when some of the design parameters are changed.

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