arXiv subjects

D. Noll

Publications and source records attributed to D. Noll.

8 recordsLinked to original sources

arXiv2019

Optimizing the Kreiss constant

The Kreiss constant $K(A)$ of a stable matrix $A$ conveys information about the transient behavior of system trajectories in response to initial conditions. We present an efficient way to compute the Kreiss constant $K(A)$, and we show how feedback can be employed to make the Kreiss constant $K(A_{cl})$ in closed loop significantly smaller. This is expected to reduce transients in the closed loop trajectories. The proposed approached is compared to potential competing techniques.

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arXiv2019

Optimization-based control design techniques and tools

Structured output feedback controller synthesis is an exciting recent concept in modern control design, which bridges between theory and practice in so far as it allows for the first time to apply sophisticated mathematical design paradigms like $H_\infty$- or $H_2$-control within control architectures preferred by practitioners. The new approach to structured $H_\infty$-control, developed by the authors during the past decade, is rooted in a change of paradigm in the synthesis algorithms. Structured design is no longer be based on solving algebraic Riccati equations or matrix inequalities. Instead, optimization-based design techniques are required. In this essay we indicate why structured controller synthesis is central in modern control engineering. We explain why non-smooth optimization techniques are needed to compute structured control laws, and we point to software tools which enable practitioners to use these new tools in high technology applications.

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arXiv2018

Non-polyhedral extensions of the Frank-and-Wolfe theorem

In 1956 Marguerite Frank and Paul Wolfe proved that a quadratic function which is bounded below on a polyhedron $P$ attains its infimum on $P$. In this work we search for larger classes of sets $F$ with this Frank-and-Wolfe property. We establish the existence of non-polyhedral Frank-and-Wolfe sets, obtain internal characterizations by way of asymptotic properties, and investigate stability of the Frank-and-Wolfe class under various operations.

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arXiv2018

Non-smooth optimization for robust control of infinite-dimensional systems

We use a non-smooth trust-region method for $H_\infty$-control of infinite-dimensional systems. Our method applies in particular to distributed and boundary control of partial differential equations. It is computationally attractive as it avoids the use of system reduction or identification. For illustration the method is applied to control a reaction-convection-diffusion system, a Van de Vusse reactor, and to a cavity flow control problem.

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arXiv2017

Structured H-infinity control of infinite dimensional systems

We develop a novel frequency-based H-infinity control method for a large class of infinite-dimensional Linear-Time-Invariant systems in transfer function form. Major benefits of our approach is that reduction or identification techniques are not needed thereby avoiding possible distortions. It can exploit either transfer function models or input/output frequency response data when available. It computes simple practical controllers of any size and structure. We use a non-smooth trust-region method to compute arbitrarily structured locally optimal H-infinity controllers for a frequency sampled approximation of the underlying infinite-dimensional H-infinity problem in such a way that exponential stability in closed-loop is guaranteed, and the optimal value of the approximation captures the value of the infinite-dimensional problem within a prior tolerance level. We demonstrate the versatility and practicality of our method on a variety of infinite-dimensional H-infinity synthesis problems, including distributed and boundary control of PDEs, control of dead time and delay systems, and using a rich testing set.

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arXiv2014

Parametric robust structured control design

We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case $H_\infty$ norm over a pre-specified set of uncertain parameters. At the core of our method is a nonsmooth minimization method tailored to functions which are semi-infinite minima of smooth functions. A rich test bench and a more detailed example illustrate the potential of the technique, which can deal with complex problems involving multiple possibly repeated uncertain parameters.

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arXiv2014

Nonconvex bundle method with application to a delamination problem

Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer adhesive between the bonded bodies, we consider the problem of computing the propagation of the crack front and the stress field along the contact boundary. This leads to a hemivariational inequality, which after discretization by finite elements we solve by a nonconvex bundle method, where upper-$C^1$ criteria have to be minimized. As this is in contrast with other classes of mechanical problems with non-monotone friction laws and in other applied fields, where criteria are typically lower-$C^1$, we propose a bundle method suited for both types of nonsmoothness. We prove its global convergence in the sense of subsequences and test it on a typical delamination problem of material sciences.

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arXiv2014

On the local convergence of the Douglas-Rachford algorithm

We discuss the Douglas-Rachford algorithm to solve the feasibility problem for two closed sets $A,B$ in $\mathbb{R}^d$. We prove its local convergence to a fixed point when $A,B$ are finite unions of convex sets. We also show that for more general nonconvex sets the scheme may fail to converge and start to cycle, and may then even fail to solve the feasibility problem.

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