State-space &amp;#956;-analysis for an experimental drive-by-wire vehicle

SUMMARY A non‐smooth optimization technique to directly compute a lower bound on the skew structured singular value ν is developed. As corroborated by several real‐world challenging applications, the proposed technique can provide tighter lower bounds when compared with currently available techniques. Moreover, in many cases, the determined lower bound equals the true value of ν. Thanks to the efficiency of the non‐smooth technique, the algorithm can be applied to problems involving even a significant number of uncertain parameters. Another appealing feature of the proposed non‐smooth approach is that the dimension of repeated scalar uncertainties in the overall structured uncertainty matrix has little impact on the computational time. The technique can be used to compute a lower bound on the structured singular value μ as well. Copyright © 2012 John Wiley & Sons, Ltd.

A MathClass-rel\in {double-struckR}^{n MathClass-bin\times n}

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Section: Non‐smooth Lower Boundmentioning

confidence: 99%

A non‐smooth lower bound on ν

Lemos

Simões

Apkarian

2012

“…Standard NLP solvers designed for smooth optimization problems will then encounter numerical difficulties, which lead to deadlock or convergence to non‐optimal points. For instance, Halton et al report this type of phenomenon and observe that convergence fails in the vast majority of cases.…”

Section: Problem Specificationmentioning

confidence: 99%

Worst‐case stability and performance with mixed parametric and dynamic uncertainties

Apkarian

Noll

2016

Summary This work deals with computing the worst‐case stability and the worst‐case H∞ performance of linear time‐invariant systems subject to mixed real‐parametric and complex‐dynamic uncertainties in a compact parameter set. Our novel algorithmic approach is tailored to the properties of the nonsmooth worst‐case functions associated with stability and performance, and this leads to a fast and reliable optimization method, which finds good lower bounds of μ. We justify our approach theoretically by proving a local convergence certificate. Because computing μ is known to be NP‐hard, our technique should be used in tandem with a classical μ upper bound to assess global optimality. Extensive testing indicates that the technique is practically attractive. Copyright © 2016 John Wiley & Sons, Ltd.

“…Discontinuities of this nature are especially evident for lightly damped flexible systems . This therefore has contributed to the adoption of state‐space and frequency interval approaches to determine the supremum of real μ . In particular, the result from provides a useful approach to subdivide a frequency range of interest into a union of predefined frequency intervals.…”

Section: Introductionmentioning

confidence: 99%

Computation of the real structured singular value via pole migration

Iordanov

Halton

2014

Self Cite

SUMMARYThe paper introduces a new computationally efficient algorithm to determine a lower bound on the real structured singular value µ. The algorithm is based on a pole migration approach where an optimization solver is used to compute a lower bound on real µ independent of a frequency sweep. A distinguishing feature of this algorithm from other frequency independent one-shot tests is that multiple localized optima (if they exist) are identified and returned from the search. This is achieved by using a number of alternative methods to generate different initial conditions from which the optimization solver can initiate its search from. The pole migration algorithm presented has also been extended to determine lower bounds for complex parametric uncertainties as well as full complex blocks. However the results presented are for strictly real and repeated parametric uncertainty problems as this class of problem is the focus of this paper and are in general the most difficult to solve.