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Dive into the research topics where Dominikus Noll is active.

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Featured researches published by Dominikus Noll.


Siam Journal on Control and Optimization | 2001

Robust Control via Sequential Semidefinite Programming

B. Fares; Dominikus Noll; Pierre Apkarian

This paper discusses nonlinear optimization techniques in robust control synthesis, with special emphasis on design problems which may be cast as minimizing a linear objective function under linear matrix inequality (LMI) constraints in tandem with nonlinear matrix equality constraints. The latter type of constraints renders the design numerically and algorithmically difficult. We solve the optimization problem via sequential semidefinite programming (SSDP), a technique which expands on sequential quadratic programming (SQP) known in nonlinear optimization. Global and fast local convergence properties of SSDP are similar to those of SQP, and SSDP is conveniently implemented with available semidefinite programming (SDP) solvers. Using two test examples, we compare SSDP to the augmented Lagrangian method, another classical scheme in nonlinear optimization, and to an approach using concave optimization.


International Journal of Control | 2001

An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory

Bassem Fares; Pierre Apkarian; Dominikus Noll

We present a new approach to a class of non-convex LMI-constrained problems in robust control theory. The problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality (LMI) constraints in tandem with non-convex constraints related to rank deficiency conditions. We solve these problems using an extension of the augmented Lagrangian technique. The Lagrangian function combines a multiplier term and a penalty term governing the non-convex constraints. The LMI constraints, due to their special structure, are retained explicitly and not included in the Lagrangian. Global and fast local convergence of our approach is then obtained either by an LMI-constrained Newton type method including line search or by a trust-region strategy. The method is conveniently implemented with available semi-definite programming (SDP) interior-point solvers. We compare its performance to the wellknown D - K iteration scheme in robust control. Two test problems are investigated and demonstrate the power and efficiency of our approach.


Siam Journal on Control and Optimization | 2008

Mixed

Pierre Apkarian; Dominikus Noll; Aude Rondepierre

We present a new approach to mixed


Siam Journal on Control and Optimization | 2006

H_2/H_\infty

Pierre Apkarian; Dominikus Noll

H_2/H_\infty


IEEE Transactions on Nuclear Science | 1999

Control via Nonsmooth Optimization

T. Farncombe; Anna Celler; Dominikus Noll; J. Maeght; R. Harrop

output feedback control synthesis. Our method uses nonsmooth mathematical programming techniques to compute locally optimal


Siam Journal on Optimization | 2005

Controller Design via Nonsmooth Multidirectional Search

Dominikus Noll; Mounir Torki; Pierre Apkarian

H_2/H_\infty


European Journal of Control | 2004

Dynamic SPECT imaging using a single camera rotation (dSPECT)

Pierre Apkarian; Dominikus Noll; Jean-Baptiste Thevenet; Hoang Duong Tuan

-controllers, which may have a predefined structure. We prove global convergence of our method and present tests to validate it numerically.


conference on decision and control | 2009

Partially Augmented Lagrangian Method for Matrix Inequality Constraints

Pierre Apkarian; Dominikus Noll; Aude Rondepierre

We propose an algorithm which combines multidirectional search (MDS) with nonsmooth optimization techniques to solve difficult problems in automatic control. Applications include static and fixed-order output feedback controller design, simultaneous stabilization,


European Journal of Control | 2006

A Spectral Quadratic-SDP Method with Applications to Fixed-Order H2 and H∞ Synthesis

Pierre Apkarian; Dominikus Noll

H_2/H_\infty


Physics in Medicine and Biology | 2000

Mixed H 2 /H ∞ control via nonsmooth optimization

Anna Celler; T. Farncombe; C Bever; Dominikus Noll; J Maeght; R. Harrop; D Lyster

-synthesis, and much else. We show how to combine direct search techniques with nonsmooth descent steps in order to obtain convergence certificates in the presence of nonsmoothness. Our technique is efficient when small and medium size controllers for plants with large state dimension are sought. Our numerical testing includes several benchmark examples. For instance, our algorithm needs 0.41\,s to compute a static output feedback stabilizing controller for the Boeing 767 flutter benchmark problem [E. E. J. Davison, IFAC Technical Committee Reports, Pergamon Press, Oxford, 1990], a system with 55 states. The first static controller without performance specifications for this system was obtained in [J. Burke, A. Lewis, and M. Overton, SIAM J. Optim., 15 (2003), pp. 751-779].

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Anna Celler

University of British Columbia

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Pierre Apkarian

Community emergency response team

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Heinz H. Bauschke

University of British Columbia

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Aude Rondepierre

Institut de Mathématiques de Toulouse

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J. Maeght

University of British Columbia

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R. Harrop

Simon Fraser University

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Minh N. Dao

Hanoi National University of Education

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Amira Rachah

Paul Sabatier University

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