Abstract
System design in presence of uncertainty calls for experimentation, and a question that arises naturally is: how many experiments are needed to come up with a system meeting certain performance requirements?
This contribution represents an attempt to answer this fundamental question. Results are con- fined to a specific set-up where adaptation is performed according to a worst-case perspective, but many considerations and reflections are central to adaptation in general.
This work is supported by MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca) under the project Identification and adaptive control of industrial systems and by CNR-IEIIT.
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References
Sastry S., Bodson M. (1994) Adaptive Control: Stability, Convergence, and Robustness. Prentice-Hall.
Astrom K.J., Wittenmark B. (1994) Adaptive Control. Addison-Wesley.
Bittanti S., Picci G. eds. (1996) Identification, Adaptation, Learning. The science of learning models from data. Springer-Verlag, Berlin, Computer and Systems Science Series, Vol. 153.
Landau I.D., Lozano R., M’Saad M. (1998) Adaptive Control. Springer-Verlag.
Haykin S. (2002) Adaptive Filter Theory. Prentice Hall.
Polderman J.W., Willems J.C. (1998) Introduction to Mathematical Systems Theory: A Behavioral Approach. Springer Verlag, New York.
Calafiore G., Campi M.C. (2005) Uncertain convex programs: randomized solutions and confidence levels. Math. Program., Ser. A 102: 25–46.
Calafiore G., Campi M.C. (2006) The scenario approach to robust control design. IEEE Trans. on Automatic Control 51(5):742–753.
Campi M.C., Garatti S. (2007) The exact feasibility of randomized solutions of convex programs. Internal report, University of Brescia, Italy.
Vapnik V.N. (1998) Statistical Learning Theory. John Wiley & Sons.
Vidyasagar M. (2001) Randomized algorithms for robust controller synthesis using statistical learning theory. Automatica 37(10):1515–1528.
Campi M.C., Prandini M. (2003) Randomized algorithms for the synthesis of cautious adaptive controllers. Systems & Control Letters 49(1):21–36.
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Bittanti, S., Campi, M.C., Prandini, M. (2007). How Many Experiments Are Needed to Adapt?. In: Chiuso, A., Pinzoni, S., Ferrante, A. (eds) Modeling, Estimation and Control. Lecture Notes in Control and Information Sciences, vol 364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73570-0_2
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DOI: https://doi.org/10.1007/978-3-540-73570-0_2
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