PIETOOLS 2025: User Manual
Sachin Shivakumar, Declan Jagt, Danilo Braghini, Amritam Das, Yulia Peet, Matthew Peet
TL;DR
PIETOOLS 2025 is a MATLAB toolbox designed for analyzing and controlling Partial Integral Equations, providing features like conversion, stability analysis, control design, and simulation, with a focus on user guidance and foundational workflows.
Contribution
This manual introduces the comprehensive features of PIETOOLS 2025, facilitating the analysis and control of PIEs with practical examples for first-time users.
Findings
Effective conversion of coupled ODE-PDEs to PIEs
Tools for stability and input-output analysis of PIEs
Capabilities for designing optimal observers and controllers
Abstract
The PIETOOLS 2025 User Manual describes all the features of version 2025 of the MATLAB toolbox PIETOOLS for the analysis and control of Partial Integral Equations (PIEs). The manual is aimed to guide, with examples, first-time users to four fundamental features of PIETOOLS: converting coupled ODE-PDEs, DDEs, DDFs, etc., to PIE representation; analysis of stability and input-output properties of PIEs; design of optimal observers and controllers for PIEs; simulation of open- and closed-loop PIE systems. The use of PIETOOLS is not limited to the features described above. However, the manual focuses on these features to provide a holistic understanding of the workflow of PIETOOLS, which will serve as a foundation to develop more complicated programs, for example, the design of boundary feedback controllers, robust observers, robust controllers, etc..
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStability and Controllability of Differential Equations · Model Reduction and Neural Networks · Modeling and Simulation Systems