IQC analysis and synthesis via nonsmooth optimization

Apkarian, Pierre; Noll, Dominikus

doi:10.1016/j.sysconle.2006.06.008

Cited by 40 publications

(31 citation statements)

References 22 publications

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“…See [10,8] for stabilization problems, [4,5,20,3,11] for H ∞ synthesis, and [3,6] for design with IQCs. These techniques are in our opinion a valuable addition to the designer's toolkit:…”

Section: Introductionmentioning

confidence: 99%

Control design in the time and frequency domain using nonsmooth techniques

Bompart

Apkarian

Noll

2008

Systems & Control Letters

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Significant progress in control design has been achieved by the use of nonsmooth and semiinfinite mathematical programming techniques. In contrast with LMI or BMI approaches, these new methods avoid the use of Lyapunov variables, which gives them two major strategic advances over matrix inequality methods. Due to the much smaller number of decision variables, they do not suffer from size restrictions, and they are much easier to adapt to structural constraints on the controller. In this paper, we further develop this line and address both frequency-and time-domain design specifications by means of a nonsmooth algorithm general enough to handle both cases. Numerical experiments are presented for reliable or fault-tolerant control, and for time response shaping.

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Section: Introductionmentioning

confidence: 99%

Control design in the time and frequency domain using nonsmooth techniques

Bompart

Apkarian

Noll

2008

Systems & Control Letters

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“…On the other hand, the design variables may be few. Attacking robust control synthesis problems directly via their nonsmooth models has gained increasing attention due to the challenge of largescale semidefinite programming (Apkarian and Noll, 2006a, 2006cBurke, Lewis, & Overton, 2004a;Burke, Henrion, Lewis, & Overton, 2006b). How analytically and computationally challenging is this direct approach?…”

Section: Nonsmooth Design and Lmismentioning

confidence: 99%

Nonsmooth optimization and robust control

Lewis

2007

Annual Reviews in Control

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Many questions of robust control analysis and synthesis fundamentally involve nonsmooth sets and functions, and their variational properties. Central examples include distances to instability and uncontrollability, the H 1 norm, and pseudospectra. This plenary presentation at the Fifth IFAC Symposium on Robust Control Design (2006), surveys what current ideas from nonsmooth analysis say about the structure and conditioning of such functions and sets, and their numerical optimization. The presentation focuses on notions of nonsmooth derivatives and regularity and on structural tools such as partial smoothness and semi-algebraic techniques, illustrating how each idea helps in analysis and algorithm design. This survey relies heavily on joint work of the author with J.V. Burke (University of Washington) and M.L. Overton (Courant Institute). #

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“…Extensions to robust performance and synthesis have also proven effective [1], [6]. This paper presents an IQC-based analysis technique to analyze the input/output gain properties of interconnections of locally stable subsystems.…”

Section: Introductionmentioning

confidence: 99%

L<inf>2</inf> gain verification for interconnections of locally stable systems using integral quadratic constraints

Summers

Packard

2010

49th IEEE Conference on Decision and Control (CDC)

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The paper establishes conditions which certify a local L 2 gain for interconnections of locally stable systems. The approach involves improvements to local L 2 gain estimation using reachability calculations. From these improved calculations, families of local integral quadratic constraints (IQCs) can be obtained for a fixed nonlinear dynamical system. Finally, the local IQCs are used to establish a local L 2 gain using a statespace formulation of the IQC robust performance theorem.

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IQC analysis and synthesis via nonsmooth optimization

Cited by 40 publications

References 22 publications

Control design in the time and frequency domain using nonsmooth techniques

Control design in the time and frequency domain using nonsmooth techniques

Nonsmooth optimization and robust control

L<inf>2</inf> gain verification for interconnections of locally stable systems using integral quadratic constraints

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