Computation of the robustness margin with the skewed μ tool

Ferreres, G.; Fromion, Vincent

doi:10.1016/s0167-6911(97)00075-3

Cited by 47 publications

(33 citation statements)

References 6 publications

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“…The aim here is to compare the methods of this paper with existing ones, in the specific context of a high order flexible system with numerous parametric uncertainties, so that only polynomialtime techniques are considered here [7,9,10].…”

Section: A Brief Comparison With Existing Methodsmentioning

confidence: 99%

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Robustness analysis of flexible structures: practical algorithms

Ferreres

Magni

Biannic

2003

Intl J Robust & Nonlinear

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SUMMARYWhen analysing the robustness properties of a flexible system, the classical solution, which consists of computing lower and upper bounds of the structured singular value (s.s.v.) at each point of a frequency gridding, appears unreliable. This paper describes two algorithms, based on the same technical result: the first one directly computes an upper bound of the maximal s.s.v. over a frequency interval, while the second one eliminates frequency intervals, inside which the s.s.v. is guaranteed to be below a given value. Various strategies are then proposed, which combine these two techniques, and also integrate methods for computing a lower bound of the s.s.v. The computational efficiency of the scheme is illustrated on a realworld application, namely a telescope mock-up which is significant of a high order flexible system.

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Section: A Brief Comparison With Existing Methodsmentioning

confidence: 99%

“…The approach of Reference [9] introduces frequency as an additional uncertainty (see also Reference [11]), so that the exact value of the maximal s.s.v. over a frequency interval can be computed as the solution of an augmented skewed m problem.…”

Section: A Brief Comparison With Existing Methodsmentioning

confidence: 99%

Robustness analysis of flexible structures: practical algorithms

Ferreres

Magni

Biannic

2003

Intl J Robust & Nonlinear

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“…Given an accurate description of the parameter distribution, its contribution of to each pathway and subsequently the transition amplitude and probability can be determined asymptotically up to a significant Dyson order M . Analogous to classical robust control [25][26][27][28][29], given the noisy distribution of the input parameters, a measure of robustness can be expressed in terms of the moments of the quantum control objective (commonly, first and second).…”

Section: Formulation Of Robustness Criteriamentioning

confidence: 99%

“…with U ji (T, α) given in equation (7) Calculation of all moments of the control and system parameters can be computed once and used where they appear in the moment expressions (25) and (28). Given a particular distribution of a parameter, for e.g.…”

Section: Formulation Of Robustness Criteriamentioning

confidence: 99%

Robustness of controlled quantum dynamics

Koswara

Chakrabarti

2014

Phys. Rev. A

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Control of multi-level quantum systems is sensitive to implementation errors in the control field and uncertainties associated with system Hamiltonian parameters. A small variation in the control field spectrum or the system Hamiltonian can cause an otherwise optimal field to deviate from controlling desired quantum state transitions and reaching a particular objective. An accurate analysis of robustness is thus essential in understanding and achieving model-based quantum control, such as in control of chemical reactions based on ab initio or experimental estimates of the molecular Hamiltonian. In this paper, theoretical foundations for quantum control robustness analysis are presented from both a distributional perspective -in terms of moments of the transition amplitude, interferences, and transition probability -and a worst-case perspective. Based on this theory, analytical expressions and a computationally efficient method for determining the robustness of coherently controlled quantum dynamics are derived. The robustness analysis reveals that there generally exists a set of control pathways that are more resistant to destructive interferences in the presence of control field and system parameter uncertainty. These robust pathways interfere and combine to yield a relatively accurate transition amplitude and high transition probability when uncertainty is present.

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“…should be computed on a continuum of frequencies, but the most common practice is to compute it on each point of a frequency gridding. The regularity assumption, which is implicitly made, appears true in most practical examples, except in very speci"c "elds such as the control of #exible structures [17,18,11]. Our method can moreover use a "ne frequency gridding, since e$cient software tools exist for solving large dimension LP problems.…”

Section: Remarkmentioning

confidence: 99%