Ph.D. received on: 8/7/1997

E-mail: garulli@ing.unisi.it

Tutor: Prof. Antonio Vicino, Università di Siena
           Prof. Giovanni Zappa, Università di Firenze

 
 

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Set-membership identification and estimation techniques   ___________________________________________________________________________________________________________

Advisor:

Prof. Antonio Vicino, Università di Siena

Summary:

The main difference between the deterministic approach and the classic stochastic approach to estimation problems, lies in the hypothesis on the uncertainty affecting the unknown quantities to be estimated. In fact, it is assumed that the uncertainty is unknown-but-bounded, i.e. no information concerning its statistic properties is available, while an upper bound on some suitable measure (norm) of the uncertainty is given. In this setting, the set-membership approach aims at characterizing the feasible estimate set, which contains all the unknown problem elements compatible with the available observations, the uncertainty bound and the a priori information.
This thesis describes the main features of the set-membership approach and presents some interesting applications in parametric identification and state estimation of linear dynamic systems. First, the available techniques for the approximation of feasible sets are reviewed. In particular, ellipsoidic algorithms are considered. Then, some algorithms for recursive approximation based on parallelotopes are presented. Simulation results show that parallelotopic algorithms provide better approximations (in terms of the volume of the estimated set), and do not require a greater computational effort with respect to other existing solutions. Moreover, parallelotopic approximations are particularly efficient when block processing of the available measurements is allowed.
The second part of the thesis addresses the analysis of some classes of pointwise estimators and studies their role in the set-membership context. Specific attention is devoted to “mixed” estimation problems, in which the knowledge of a bound on the uncertainty is explicitely accounted for in the estimation criterion, and to the characterization of reduced complexity estimators.

 
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