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Approximate computation of storage functions for discrete-time systems using sum-of-squares techniques

Title data

Pirkelmann, Simon ; Angeli, David ; Grüne, Lars:
Approximate computation of storage functions for discrete-time systems using sum-of-squares techniques.
Bayreuth , 2019 . - 9 p.

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Model predictive PDE control for energy efficient building operation: economic model predictive control and time-varying systemsGR 1569/16-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

In this paper we present a method for automated verification of dissipativity by numerical means for discrete time systems with polynomial dynamics and stage cost. It relies on sum-of-squares techniques in order to compute storage functions that satisfy a dissipation inequality. The method can also be used to treat systems subject to constraints. Moreover, an Taylor approximation based extension to more general nonlinear stage costs is presented which enables the computation of approximate local storage functions.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
Additional notes: Major parts of this work were conducted during a visit of the first author at Imperial College in London, UK.
Keywords: Dissipativity; Storage Functions; Sum-of-Squares; Polynomial Systems; Taylor Approximation
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 16 Feb 2019 22:00
Last Modified: 14 Mar 2019 13:43
URI: https://eref.uni-bayreuth.de/id/eprint/47444