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Optimal supervisory control of stochastic linear systems: a cost-biased approach

In the presence of large uncertainty, traditional control methodologies based on a single controller often do not provide satisfactory performance, not even guarantee stability of the closed-loop system. This calls for the design of a family of candidate controllers as well as a logic-based supervisor to orchestrate the switching among them so as to achieve the desired performance. The analysis of the resulting hybrid system requires specialized tools. In this talk, we deal with the problem of controlling an imprecisely modeled linear system affected by a stochastic - possibly unbounded - noise. We design a supervisory control system which proves to be successful in stabilizing the switched closed-loop system, and in achieving optimal performance in terms of a certain long-run average quadratic cost criterion. The switching control methodology adopted here is "estimator based", as it relies on a parameter estimation procedure in carrying out the controller selection. Stability is ensured by choosing the switching time instants so as to exponentially stabilize the autonomous estimated model according to an adaptive version of the so-called "dwell time" logic. Optimality is instead achieved by introducing in the monitoring signal for parameter estimation a cost-biasing term which favors the parameters with smaller cost. An appropriate balance between an integral norm of the output estimation error and the cost-biasing term allows us to prove that the estimated model resembles the behavior of the process, at least in closed-loop, and hence the actually incurred cost is minimum.

Type of Seminar:
Minisymposium on Analysis and Control of Dynamical Systems
Dr. Maria Prandini
Universitą degli Studi di Brescia Via Branze, 38 25123 Brescia Italy
Dec 19, 2000   13:15

ETH Zentrum, Building VAW, Room B1, Gloriastrasse 37-39, 8006 Zurich
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Maria Prandini received the Laurea and the Ph.D. degree in electrical engineering respectively from the Politecnico of Milano, in 1994, and from the University of Brescia, in 1998. From March to July 1998, she was a visiting scholar at Delft University of Technology, the Netherlands. She also held postdoctoral research appointments with the Electrical Engineering and Computer Sciences Department, UC Berkeley (August 1998-October 2000), and with the Department of Electronics for Automation, University of Brescia (September 1998-March 2000). From April 2000 she has been a research fellow at the University of Brescia. Her research interests include identification and adaptive control, statistical learning theory, hybrid modeling and control, game theory, and their application to digital communication, air traffic management, and coordination and control of multi-agent systems.