40 research outputs found
Quantum computing through the lens of control: A tutorial introduction
Quantum computing is a fascinating interdisciplinary research field that
promises to revolutionize computing by efficiently solving previously
intractable problems. Recent years have seen tremendous progress on both the
experimental realization of quantum computing devices as well as the
development and implementation of quantum algorithms. Yet, realizing
computational advantages of quantum computers in practice remains a widely open
problem due to numerous fundamental challenges. Interestingly, many of these
challenges are connected to performance, robustness, scalability, optimization,
or feedback, all of which are central concepts in control theory. This paper
provides a tutorial introduction to quantum computing from the perspective of
control theory. We introduce the mathematical framework of quantum algorithms
ranging from basic elements including quantum bits and quantum gates to more
advanced concepts such as variational quantum algorithms and quantum errors.
The tutorial only requires basic knowledge of linear algebra and, in
particular, no prior exposure to quantum physics. Our main goal is to equip
readers with the mathematical basics required to understand and possibly solve
(control-related) problems in quantum computing. In particular, beyond the
tutorial introduction, we provide a list of research challenges in the field of
quantum computing and discuss their connections to control
Robust data-driven control for nonlinear systems using the Koopman operator
Data-driven analysis and control of dynamical systems have gained a lot of
interest in recent years. While the class of linear systems is well studied,
theoretical results for nonlinear systems are still rare. In this paper, we
present a data-driven controller design method for discrete-time control-affine
nonlinear systems. Our approach relies on the Koopman operator, which is a
linear but infinite-dimensional operator lifting the nonlinear system to a
higher-dimensional space. Particularly, we derive a linear fractional
representation of a lifted bilinear system representation based on measured
data. Further, we restrict the lifting to finite dimensions, but account for
the truncation error using a finite-gain argument. We derive a linear matrix
inequality based design procedure to guarantee robust local stability for the
resulting bilinear system for all error terms satisfying the finite-gain bound
and, thus, also for the underlying nonlinear system. Finally, we apply the
developed design method to the nonlinear Van der Pol oscillator.Comment: Accepted for presentation at the IFAC World Congress 202
Control of bilinear systems using gain-scheduling: Stability and performance guarantees
In this paper, we present a state-feedback controller design method for
bilinear systems. To this end, we write the bilinear system as a linear
fractional representation by interpreting the state in the bilinearity as a
structured uncertainty. Based on that, we derive convex conditions in terms of
linear matrix inequalities for the controller design, which are efficiently
solvable by semidefinite programming. Further, we prove asymptotic stability
and quadratic performance of the resulting closed-loop system locally in a
predefined region. The proposed design uses gain-scheduling techniques and
results in a state feedback with rational dependence on the state, which can
substantially reduce conservatism and improve performance in comparison to a
simpler, linear state feedback. Moreover, the design method is easily adaptable
to various scenarios due to its modular formulation in the robust control
framework. Finally, we apply the developed approaches to numerical examples and
illustrate the benefits of the approach.Comment: Submitted to the 62nd IEEE Conference on Decision and Control
(CDC2023
Combining Prior Knowledge and Data for Robust Controller Design
We present a framework for systematically combining data of an unknown linear
time-invariant system with prior knowledge on the system matrices or on the
uncertainty for robust controller design. Our approach leads to linear matrix
inequality (LMI) based feasibility criteria which guarantee stability and
performance robustly for all closed-loop systems consistent with the prior
knowledge and the available data. The design procedures rely on a combination
of multipliers inferred via prior knowledge and learnt from measured data,
where for the latter a novel and unifying disturbance description is employed.
While large parts of the paper focus on linear systems and input-state
measurements, we also provide extensions to robust output-feedback design based
on noisy input-output data and against nonlinear uncertainties. We illustrate
through numerical examples that our approach provides a flexible framework for
simultaneously leveraging prior knowledge and data, thereby reducing
conservatism and improving performance significantly if compared to black-box
approaches to data-driven control
Data-driven estimation of the maximum sampling interval: analysis and controller design for discrete-time systems
This article is concerned with data-driven analysis of discrete-time systems
under aperiodic sampling, and in particular with a data-driven estimation of
the maximum sampling interval (MSI). The MSI is relevant for analysis of and
controller design for cyber-physical, embedded and networked systems, since it
gives a limit on the time span between sampling instants such that stability is
guaranteed. We propose tools to compute the MSI for a given controller and to
design a controller with a preferably large MSI, both directly from a
finite-length, noise-corrupted state-input trajectory of the system. We follow
two distinct approaches for stability analysis, one taking a robust control
perspective and the other a switched systems perspective on the aperiodically
sampled system. In a numerical example and a subsequent discussion, we
demonstrate the efficacy of our developed tools and compare the two approaches.Comment: 16 pages, 4 figure, 1 table. Now contains 1) a disturbance
description via multipliers, 2) extended proofs and 3) an extensive numerical
case study, including a comparison of different data lengths, a discussion of
complexity and a comparison with set membership estimatio