A monte carlo approach to the analysis of control system robustness

Ray, Laura E.; Stengel, Robert F.

doi:10.1016/0005-1098(93)90187-x

Cited by 203 publications

(75 citation statements)

References 12 publications

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“…Formally, for any and , if then An obvious but crucial observation which follows immediately from the Chernoff bound is that is independent of the number and dimension of the uncertain blocks in the matrix and of the size of the bounding set [24], [37]; similar statements can be also made when consists of parametric uncertainty only [33]. The same conclusion holds when dealing with more sophisticated bounds arising in Learning Theory; see [40].…”

Section: Introductionmentioning

confidence: 89%

“…In fact, at the th step of the conditional method, the variables up to are given, and only the dependence on is required. In this case, (32) represents a polynomial in the variable, whose coefficients and the multiplicative constant can be easily computed according to (33) and (34), once the values of are known. 2) We observe that for the quantities and appearing in (34) and (35) can be computed recursively, so that no matrix inversion or determinant computation is required.…”

Section: Remarksmentioning

confidence: 99%

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Randomized algorithms for probabilistic robustness with real and complex structured uncertainty

Calafiore

Dabbene

Tempo

2000

IEEE Trans. Automat. Contr.

146

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Abstract-In recent years, there has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems. Unlike classical worst case methods, these algorithms provide probabilistic estimates assessing, for instance, if a certain design specification is met with a given probability. One of the advantages of this approach is that the robustness margins can be often increased by a considerable amount, at the expense of a small risk. In this sense, randomized algorithms may be used by the control engineer together with standard worst case methods to obtain additional useful information.The applicability of these probabilistic methods to robust control is presently limited by the fact that the sample generation is feasible only in very special cases which include systems affected by real parametric uncertainty bounded in rectangles or spheres. Sampling in more general uncertainty sets is generally performed through overbounding, at the expense of an exponential rejection rate.In this paper, randomized algorithms for stability and performance of linear time invariant uncertain systems described by a general -1 configuration are studied. In particular, efficient polynomial-time algorithms for uncertainty structures 1 consisting of an arbitrary number of full complex blocks and uncertain parameters are developed.

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Section: Introductionmentioning

confidence: 89%

Section: Remarksmentioning

confidence: 99%

Randomized algorithms for probabilistic robustness with real and complex structured uncertainty

Calafiore

Dabbene

Tempo

2000

IEEE Trans. Automat. Contr.

146

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“…Ray and Stengel (1993); Tempo and Dabbene (1999); Vidyasagar and Blondel (2001) and Vidyasagar (2001). The main idea behind randomized methods is to associate a probability distribution to the uncertainty set, and to assess system performance in terms of empirical probability.…”

Section: A Probabilistic Framework For Uncertain Systemsmentioning

confidence: 99%

“…Recently, a new parallel line of research has emerged, which proposes to substitute the robust or worst-case viewpoint with a more tractable probabilistic one (Ray & Stengel, 1993; This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor R. Srikant under the direction of Editor Tamer Basar.…”

Section: Introductionmentioning

confidence: 99%

A probabilistic framework for problems with real structured uncertainty in systems and control

Calafiore

Dabbene

2002

Automatica

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The objective of this paper is twofold. First, the problem of generation of real random matrix samples with uniform distribution in structured (spectral) norm bounded sets is studied. This includes an analysis of the distribution of the singular values of uniformly distributed real matrices, and an e cient (i.e. polynomial-time) algorithm for their generation. Second, it is shown how the developed techniques may be used to solve in a probabilistic setting several hard problems involving systems subject to real structured uncertainty. ?

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“…Significant contributions have been made by a number of researchers (see, e.g., [1,2,3,4,5], [10,11,12,13,14,15,16,17] and the reference therein). A fundamental problem in the area of probabilistic robustness analysis is to estimate the probability that a certain robustness requirement is guaranteed for an uncertain dynamic system.…”

Section: Introductionmentioning

confidence: 99%

On the binomial confidence interval and probabilistic robust control

2004

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The Clopper-Pearson confidence interval has ever been documented as an exact approach in some statistics literature. More recently, such approach of interval estimation has been introduced to probabilistic control theory and has been referred as non-conservative in control community.In this note, we clarify the fact that the so-called exact approach is actually conservative. In particular, we derive analytic results demonstrating the extent of conservatism in the context of probabilistic robustness analysis. This investigation encourages seeking better methods of confidence interval construction for robust control purpose.

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A monte carlo approach to the analysis of control system robustness

Cited by 203 publications

References 12 publications

Randomized algorithms for probabilistic robustness with real and complex structured uncertainty

Randomized algorithms for probabilistic robustness with real and complex structured uncertainty

A probabilistic framework for problems with real structured uncertainty in systems and control

On the binomial confidence interval and probabilistic robust control

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