PIETOOLS: A Matlab Toolbox for Manipulation and Optimization of Partial Integral Operators

Sachin Shivakumar, Amritam Das, Matthew M. Peet

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

16 Citaten (Scopus)

Samenvatting

In this paper, we present PIETOOLS, a MATLAB toolbox for the construction and handling of Partial Integral (PI) operators. The toolbox introduces a new class of MATLAB object, opvar, for which standard MATLAB matrix operation syntax (e.g. +, ' etc.) is defined. PI operators are a generalization of bounded linear operators on infinite-dimensional spaces that form a-subalgebra with two binary operations (addition and composition) on the space × L2. These operators frequently appear in analysis and control of infinite-dimensional systems such as Partial Differential Equations (PDE) and Timedelay systems (TDS). Furthermore, PIETOOLS can: declare opvar decision variables, add operator positivity constraints, declare an objective function, and solve the resulting optimization problem using a syntax similar to the sdpvar class in YALMIP. Use of the resulting Linear Operator Inequalities (LOI) are demonstrated on several examples, including stability analysis of a PDE, bounding operator norms, and verifying integral inequalities. The result is that PIETOOLS, packaged with SOSTOOLS and MULTIPOLY, offers a scalable, user-friendly and computationally efficient toolbox for parsing, performing algebraic operations, setting up and solving convex optimization problems on PI operators.

Originele taal-2Engels
Titel2020 American Control Conference, ACC 2020
UitgeverijInstitute of Electrical and Electronics Engineers
Pagina's2667-2672
Aantal pagina's6
ISBN van elektronische versie9781538682661
DOI's
StatusGepubliceerd - jul. 2020
Evenement2020 American Control Conference, ACC 2020 - Denver, Verenigde Staten van Amerika
Duur: 1 jul. 20203 jul. 2020
http://acc2020.a2c2.org/

Congres

Congres2020 American Control Conference, ACC 2020
Verkorte titelACC 2020
Land/RegioVerenigde Staten van Amerika
StadDenver
Periode1/07/203/07/20
Internet adres

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