Abstract
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.
Original language | English |
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Title of host publication | 2020 American Control Conference, ACC 2020 |
Publisher | Institute of Electrical and Electronics Engineers |
Pages | 2667-2672 |
Number of pages | 6 |
ISBN (Electronic) | 9781538682661 |
DOIs | |
Publication status | Published - Jul 2020 |
Event | 2020 American Control Conference, ACC 2020 - Denver, United States Duration: 1 Jul 2020 → 3 Jul 2020 http://acc2020.a2c2.org/ |
Conference
Conference | 2020 American Control Conference, ACC 2020 |
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Abbreviated title | ACC 2020 |
Country/Territory | United States |
City | Denver |
Period | 1/07/20 → 3/07/20 |
Internet address |