Adaptive Approximation of Uncertainty Sets for Linear Regression Models
This chapter deals with the problem of uncertainty evaluation in linear regression models, representing either purely parametric models or mixed parametric/non-parametric (restricted complexity) models. The hypothesis is that disturbance information and prior knowledge on the unmodeled dynamics are available as deterministic bounds. A procedure is proposed for constructing recursively an outer bounding parallelotopic estimate of the parameter uncertainty set, which can be considered as an alternative description to commonly used ellipsoidal approximations. This new type of approximation is motivated by recent developments in the robust control field, where descriptions like hyperrectangular or polytopic domains have led to appealing stability and performance robustness properties of uncertain feedback systems.
KeywordsLinear Regression Model Supporting Hyperplane Unmodeled Dynamic Ellipsoidal Approximation Nonparametric Part
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- 2.M. Gevers, in: Proceedings of the 9th IFAC Symposium on Identification and System Parameter Estimation, Budapest, Hungary, pp. 1-10 (1991).Google Scholar
- 5.D. N. C. Tse, M. A. Dahleh and J. N. Tsitsiklis, in: Proceedings of the International Workshop on Robust Control, CRC Press, San Antonio, TX, pp. 311–328 (1991).Google Scholar
- 9.R. C. Younce and C. E. Rohrs, in: Proceedings of the 29th CDC, Honolulu, HI, pp. 3154-3161 (1990).Google Scholar
- 13.J. C. Doyle, J. E. Wall and G. Stein, in: Proceedings of the 21st IEEE CDC, Orlando, FL, pp. 629-636 (1982).Google Scholar
- 19.A. Vicino and G. Zappa, Sequential Approximation of Parameter Sets for Identification with Parametric and Nonparametric Uncertainty, Tech. Rep. DSI/RT-12/93, Università di Firenze, Firenze, Italy (1993).Google Scholar