E.W. Bai, R. Tempo, and M. Fu, "Worst Case Properties of the Uniform Distribution and Randomized Algorithms for Robustness Analysis," Mathematics of Control, Signals, and Systems, vol. 11, pp. 183-196, 1998. Home/Search Document Details and Download
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Fast Algorithms for Exact and Approximate Feasibility of.. - Giuseppe Calafiore And (Correct)
.... Delta over its support set Delta, and that it is possible to generate samples of Delta according to this probability distribution. We will not discuss here issues related to the choice of the probability distribution f Delta . A natural choice (which also has theoretical rationale behind, see [2]) is to assume uniform distribution in the space of Delta. In this case, efficient algorithms for the generation of samples on Delta are discussed in depth in [7] Weintroduce a scalar function (x# Delta)# defined as (x# Delta) jjF (x# Delta)jj# (6) where the notation A indicates ....
E.W. Bai, R. Tempo, and M. Fu, "Worst Case Properties of the Uniform Distribution and Randomized Algorithms for Robustness Analysis," Mathematics of Control, Signals, and Systems, vol. 11, pp. 183-196, 1998.
Statistical Learning Control of Uncertain Systems: It.. - Koltchinskii.. (1999) (1 citation) (Correct)
....probabilistic tools [21] 34] 66] with ideas advanced during the 1960s and 1970s [63] on the theory of empirical processes and statistical learning. In control theory, some of the original (Monte Carlo) ideas have already been used by Lee and Poolla [45] Ray and Stengel [52] Tempo et al. [6], 59] 60] Barmish et al. 7] 8] 9] 10] Chen and Zhou [18] 19] 20] and by Khargonakar and Tikku [40] to solve robust analysis problems while Vidyasagar used learning theory to solve robust design problems [66] 68] Unfortunately, and as acknowledged by the various authors, ....
E. Bai, R. Tempo, and M. Fu. Worst case properties of the uniform distribution and randomized algorithms for robustness analysis. In Proc. IEEE American Control Conf., pages 861-865, Albuquerque, NM, 1997.
Solving strict polynomial inequalities by Bernstein expansion - Garloff, Graf (1999) (7 citations) (Correct)
....it should be noted that in contrast to symbolic methods Bernstein expansion requires a priori bounds on the design parameter range. This is not a hard restriction since the designer often can estimate the interesting parameter range. We mention a third approach, the probabilistic approach, e.g. [5, 6], to solve problems in control theory which can be formulated as systems of strict inequalities. Here again bounds on the parameter range must be known. This approach is applicable to very complex systems but it provides only probabilistic answers. Notation: For compactness, we define a ....
BAI, E.-W., TEMPO, R., and FU, M.: 'Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis', Proc. of the American Control Conference, Albuquerque, NM, 1997
Worst-Case Properties of the Uniform Distribution and.. - Bai, Tempo, Fu (1996) (3 citations) Self-citation (Bai Tempo Fu) (Correct)
....we present a numerical example showing the efficacy of this approach. In Section 5, we discuss some issues and drawbacks of the existing results and, in particular, we study cases when the bound N grows with the problem size. Finally, in Section 6 we provide conclusions; the proofs are given in [3]. 2. Worst Case Properties of the Uniform Distribution First, we define the set of allowable probability density functions on Q. Definition 2.1 Let F be the set of all bounded and (Lebesgue) measurable time invariant probability density functions f( Delta) on Q, i.e. the distribution function ....
E.-W. Bai, R. Tempo and M. Fu, "Worst-Case Properties of the Uniform Distribution and Randomized Algorithms for Robustness Analysis," CENS-CNR Report, November 1996.
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