77 research outputs found
Robust Exponential Stability and Invariance Guarantees with General Dynamic O'Shea-Zames-Falb Multipliers
We propose novel time-domain dynamic integral quadratic constraints with a
terminal cost for exponentially weighted slope-restricted gradients of not
necessarily convex functions. This extends recent results for subdifferentials
of convex function and their link to so-called O'Shea-Zames-Falb multipliers.
The benefit of merging time-domain and frequency-domain techniques is
demonstrated for linear saturated systems.Comment: This paper will appear in the Proceedings of the IFAC World Congress
202
Interacting electrons on trilayer honeycomb lattices
Few-layer graphene systems come in various stacking orders. Considering
tight-binding models for electrons on stacked honeycomb layers, this gives rise
to a variety of low-energy band structures near the charge neutrality point.
Depending on the stacking order these band structures enhance or reduce the
role of electron-electron interactions. Here, we investigate the instabilities
of interacting electrons on honeycomb multilayers with a focus on trilayers
with ABA and ABC stackings theoretically by means of the functional
renormalization group. We find different types of competing instabilities and
identify the leading ordering tendencies in the different regions of the phase
diagram for a range of local and non-local short-ranged interactions. The
dominant instabilities turn out to be toward an antiferromagnetic spin-density
wave (SDW), a charge density wave and toward quantum spin Hall (QSH) order.
Ab-initio values for the interaction parameters put the systems at the border
between SDW and QSH regimes. Furthermore, we discuss the energy scales for the
interaction-induced gaps of this model study and put them into context with the
scales for single-layer and Bernal-stacked bilayer honeycomb lattices. This
yields a comprehensive picture of the possible interaction-induced ground
states of few-layer graphene.Comment: 12 pages, 12 figure
Output-Feedback Synthesis for a Class of Aperiodic Impulsive Systems
We derive novel criteria for designing stabilizing dynamic output-feedback
controllers for a class of aperiodic impulsive systems subject to a range
dwell-time condition. Our synthesis conditions are formulated as
clock-dependent linear matrix inequalities (LMIs) which can be solved
numerically, e.g., by using matrix sum-of-squares relaxation methods. We show
that our results allow us to design dynamic output-feedback controllers for
aperiodic sample-data systems and illustrate the proposed approach by means of
a numerical example
Input-Output-Data-Enhanced Robust Analysis via Lifting
Starting from a linear fractional representation of a linear system affected
by constant parametric uncertainties, we demonstrate how to enhance standard
robust analysis tests by taking available (noisy) input-output data of the
uncertain system into account. Our approach relies on a lifting of the system
and on the construction of data-dependent multipliers. It leads to a test in
terms of linear matrix inequalities which guarantees stability and performance
for all systems compatible with the observed data if it is in the affirmative.
In contrast to many other data-based approaches, prior physical knowledge is
included at the outset due to the underlying linear fractional representation
On the exactness of a stability test for Lur'e systems with slope-restricted nonlinearities
In this note it is shown that the famous multiplier absolute stability test
of R. O'Shea, G. Zames and P. Falb is necessary and sufficient if the set of
Lur'e interconnections is lifted to a Kronecker structure and an explicit
method to construct the destabilizing static nonlinearity is presented
Gain-Scheduling Controller Synthesis for Networked Systems with Full Block Scalings
This work presents a framework to synthesize structured gain-scheduled
controllers for structured plants that are affected by time-varying parametric
scheduling blocks. Using a so-called lifting approach, we are able to handle
several structured gain-scheduling problems arising from a nested inner and
outer loop configuration with partial or full dependence on the scheduling
block. Our resulting design conditions are formulated in terms of convex linear
matrix inequalities and permit to handle multiple performance objectives.Comment: 16 pages, 4 figure
Lifting to Passivity for -Gain-Scheduling Synthesis with Full Block Scalings
We focus on the -gain-scheduling synthesis problem for
time-varying parametric scheduling blocks with scalings. Recently, we have
presented a solution of this problem for - and positive real scalings by
guaranteeing finiteness of the -norm for the closed-loop system
with suitable linear fractional plant and controller representations. In order
to reduce conservatism, we extend these methods to full block scalings by
designing a triangular scheduling function and by introducing a new lifting
technique for gain-scheduled synthesis that enables convexification
Controller Design via Experimental Exploration with Robustness Guarantees
For a partially unknown linear systems, we present a systematic control
design approach based on generated data from measurements of closed-loop
experiments with suitable test controllers. These experiments are used to
improve the achieved performance and to reduce the uncertainty about the
unknown parts of the system. This is achieved through a parametrization of
auspicious controllers with convex relaxation techniques from robust control,
which guarantees that their implementation on the unknown plant is safe. This
approach permits to systematically incorporate available prior knowledge about
the system by employing the framework of linear fractional representations
Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression
Gaussian Process Regression is a popular nonparametric regression method
based on Bayesian principles that provides uncertainty estimates for its
predictions. However, these estimates are of a Bayesian nature, whereas for
some important applications, like learning-based control with safety
guarantees, frequentist uncertainty bounds are required. Although such rigorous
bounds are available for Gaussian Processes, they are too conservative to be
useful in applications. This often leads practitioners to replacing these
bounds by heuristics, thus breaking all theoretical guarantees. To address this
problem, we introduce new uncertainty bounds that are rigorous, yet practically
useful at the same time. In particular, the bounds can be explicitly evaluated
and are much less conservative than state of the art results. Furthermore, we
show that certain model misspecifications lead to only graceful degradation. We
demonstrate these advantages and the usefulness of our results for
learning-based control with numerical examples.Comment: Contains supplementary material and corrections to the original
versio
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