Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

On Performance Guarantees for Systems with Conic Constraints

Vladu, Emil LU orcid (2025)
Abstract
In this thesis, we provide a number of novel algebraic means of certifying stability and performance for linear systems constrained in various ways by cones. The purpose is mainly threefold: to provide mathematical statements with applicative potential, to unify seemingly dissimilar results in the literature and thereby increase understanding, and to advance the state of the art on dynamical systems with conic constraints, an area of control still in its infancy. The main contributions of the five papers contained in the thesis are as follows. Paper I provides an analytical upper bound on the deviation from H-infinity optimality of a certain controller class as a function of the deviation from symmetry in the state matrix. Paper II goes on... (More)
In this thesis, we provide a number of novel algebraic means of certifying stability and performance for linear systems constrained in various ways by cones. The purpose is mainly threefold: to provide mathematical statements with applicative potential, to unify seemingly dissimilar results in the literature and thereby increase understanding, and to advance the state of the art on dynamical systems with conic constraints, an area of control still in its infancy. The main contributions of the five papers contained in the thesis are as follows. Paper I provides an analytical upper bound on the deviation from H-infinity optimality of a certain controller class as a function of the deviation from symmetry in the state matrix. Paper II goes on to establish a diagonal solution to a Riccati inequality which certifies H-infinity optimality of a particular controller both when the open-loop state matrix is symmetric and when the closed-loop system is positive. In Paper III, a necessary and sufficient condition is given in the form of a stable coefficient matrix for a nonsymmetric Riccati equation to admit a stabilizing cone-preserving solution. This result is subsequently applied in Paper IV to obtain a nonsymmetric variant of the bounded real lemma in H-infinity control on self-dual cones. Finally, Paper V establishes an equivalence between the existence of a bounded linear functional satisfying a conic inequality and the satisfaction of certain integral linear constraints on trajectories confined to a cone. This result in turn yields a non-strict version of the Kalman-Yakubovich-Popov Lemma when the cone is taken as the positive semidefinite cone, thereby serving to further bring together linear-cone theory with the dominating linear-quadratic paradigm in control. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Prof. Bamieh, Bassam, University of California at Santa Barbara , USA.
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Cone-preserving Systems, Nonsymmetric Algebraic Riccati Equations, H-infinity Control, Integral Linear Constraints, Conic Constraints
publisher
Department of Automatic Control, Lund University
defense location
Lecture Hall M:B, building M, Ole Römers väg 1, Faculty of Engineering LTH, Lund University, Lund. The dissertation will be live streamed, but part of the premises is to be excluded from the live stream. Zoom: https://lu-se.zoom.us/j/63908450978
defense date
2025-03-21 10:15:00
ISBN
978-91-8104-415-7
978-91-8104-416-4
language
English
LU publication?
yes
id
f08a1122-34e3-44d4-ae64-4c3035b848b0
date added to LUP
2025-02-24 14:47:23
date last changed
2025-04-04 15:08:09
@phdthesis{f08a1122-34e3-44d4-ae64-4c3035b848b0,
  abstract     = {{In this thesis, we provide a number of novel algebraic means of certifying stability and performance for linear systems constrained in various ways by cones. The purpose is mainly threefold: to provide mathematical statements with applicative potential, to unify seemingly dissimilar results in the literature and thereby increase understanding, and to advance the state of the art on dynamical systems with conic constraints, an area of control still in its infancy. The main contributions of the five papers contained in the thesis are as follows. Paper I provides an analytical upper bound on the deviation from H-infinity optimality of a certain controller class as a function of the deviation from symmetry in the state matrix. Paper II goes on to establish a diagonal solution to a Riccati inequality which certifies H-infinity optimality of a particular controller both when the open-loop state matrix is symmetric and when the closed-loop system is positive. In Paper III, a necessary and sufficient condition is given in the form of a stable coefficient matrix for a nonsymmetric Riccati equation to admit a stabilizing cone-preserving solution. This result is subsequently applied in Paper IV to obtain a nonsymmetric variant of the bounded real lemma in H-infinity control on self-dual cones. Finally, Paper V establishes an equivalence between the existence of a bounded linear functional satisfying a conic inequality and the satisfaction of certain integral linear constraints on trajectories confined to a cone. This result in turn yields a non-strict version of the Kalman-Yakubovich-Popov Lemma when the cone is taken as the positive semidefinite cone, thereby serving to further bring together linear-cone theory with the dominating linear-quadratic paradigm in control.}},
  author       = {{Vladu, Emil}},
  isbn         = {{978-91-8104-415-7}},
  keywords     = {{Cone-preserving Systems; Nonsymmetric Algebraic Riccati Equations; H-infinity Control; Integral Linear Constraints; Conic Constraints}},
  language     = {{eng}},
  month        = {{02}},
  publisher    = {{Department of Automatic Control, Lund University}},
  school       = {{Lund University}},
  title        = {{On Performance Guarantees for Systems with Conic Constraints}},
  url          = {{https://lup.lub.lu.se/search/files/209082002/Emil_Vladu_-_Thesis.pdf}},
  year         = {{2025}},
}