Robust finite-frequency &amp;#x210B;&lt;inf&gt;2&lt;/inf&gt; analysis

IFAC Proceedings Volumes

Hansson

Garulli

2011

Self Cite

“…The following theorem, extracted from Paganini (1997) and Masi et al (2010), utilizes this condition to provide an upper bound for ∆ * M 2 2 for any frequency and any…”

Section: An Upper Bound For the Robust H 2 Normmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the calculation of the robust finite frequency H2 norm

IFAC Proceedings Volumes

Hansson

Garulli

2011

Self Cite

“…However, the algorithm labeled Gramian-based in the paper has been entirely developed by the other authors of the paper, see Masi et al (2010). Parts of this paper has also been presented in S. Khoshfetrat Pakazad, A. Hansson, and A. Garulli.…”

Section: Robustmentioning

confidence: 99%

Divide and Conquer: Distributed Optimization and Robustness Analysis

Linköping Studies in Science and Technology. Dissertations

2015

Linköping 2015Cover illustration: A design approach for distributed optimization alogirhtms, used in papers C and F. It states that given the sparstiy graph of a coupled optimization problem, defined in Section 5.1, we can group its variables and its constituent subprobelms so that the coupling structure can be represented using a tree. We can then solve the problem distributedly using message passing, which utilizes the tree as its computational graph. To my parents AbstractAs control of large-scale complex systems has become more and more prevalent within control, so has the need for analyzing such controlled systems. This is particularly due to the fact that many of the control design approaches tend to neglect intricacies in such systems, e.g., uncertainties, time delays, nonlinearities, so as to simplify the design procedure. Robustness analysis techniques allow us to assess the effect of such neglected intricacies on performance and stability. Performing robustness analysis commonly requires solving an optimization problem. However, the number of variables of this optimization problem, and hence the computational time, scales badly with the dimension of the system. This limits our ability to analyze large-scale complex systems in a centralized manner. In addition, certain structural constraints, such as privacy requirements or geographical separation, can prevent us from even forming the analysis problem in a centralized manner.In this thesis, we address these issues by exploiting structures that are common in large-scale systems and/or their corresponding analysis problems. This enables us to reduce the computational cost of solving these problems both in a centralized and distributed manner. In order to facilitate distributed solutions, we employ or design tailored distributed optimization techniques. Particularly, we propose three distributed optimization algorithms for solving the analysis problem, which provide superior convergence and/or computational properties over existing algorithms. Furthermore, these algorithms can also be used for solving general loosely coupled optimization problems that appear in a variety of fields ranging from control, estimation and communication systems to supply chain management and economics.v Populärvetenskaplig sammanfattningRegulatorer för styrning av system är ofta designade med hjälp av en beskrivning, typiskt en matematisk modell, av det man vill styra. Dessa modeller är oftast endast approximativa beskrivningar av det verkliga systemet och därför behäftade med osäkerheter. Detta medför att det beteende man förväntar sig av ett reglerat system baserat på den matematiska modellen inte alltid stämmer överens med det observerade beteendet. Att analysera hur stor denna avvikelse kan bli kallas robusthetsanalys. Detta är ett väl studerat område för mindre och medelstora system. Dock är kunskaperna begränsade för riktigt stora system, speciellt om man inte vill göra en alltför konservativ analys. Exempel på stora system är kraftnät och flygplan. Kraftnät är stora på gr...

“…We also assume that a LFT (Linear Fractional Transformation) representation of these systems are available, which is a common assumption in many fields concerning uncertain systems, e.g., in aeronautics, Cockburn and Morton (1997); Poussot-Vassal and Roos (2012); Ferreres (2011);Zhou et al (1996). The first method combines the notion of finite-frequency Gramians, introduced in Gawronski (2000), with convex optimization tools, Boyd and Vandenberghe (2004), commonly used in robust control, and it calculates an upper bound by solving an underlying optimization problem, Masi et al (2010). The second method, provides a computationally cheaper algorithmic method for calculating such upper bounds.…”

Section: Introductionmentioning

confidence: 99%

Robust finite-frequency analysis of uncertain systems with application to flight comfort analysis

Garulli

Hansson

Control Engineering Practice

et al. 2013

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In many applications, design or analysis is performed over a finite-frequency range of interest. The importance of the H 2 norm highlights the necessity of computing this norm accordingly. This paper provides different methods for computing upper bounds of the robust finite-frequency H 2 norm for systems with structured uncertainties. An application of the robust finite-frequency H 2 norm for a comfort analysis problem of an aero-elastic model of an aircraft is also presented.