Discussion paper: A new mathematical framework for representation and analysis of coupled PDEs

Matthew M. Peet; Sachin Shivakumar; Amritam Das; Seip Weiland

doi:10.1016/j.ifacol.2019.08.023

Discussion paper: A new mathematical framework for representation and analysis of coupled PDEs

Matthew M. Peet, Sachin Shivakumar, Amritam Das, Seip Weiland

Mechanical and Aerospace Engineering

Research output: Contribution to journal › Conference article › peer-review

7 Scopus citations

Abstract

We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichlet, Neuman and mixed boundary conditions. The results in this paper apply to systems with a single spatial variable. We exploit a new concept of state for PDE systems which allows us to include the boundary conditions directly in the dynamics of the PDE. The resulting algorithms are implemented in Matlab, tested on several motivating and illustrative examples, and the codes have been posted online. Numerical testing indicates the approach has little or no conservatism for a large class of systems and can analyze systems of up to 20 coupled PDEs.

Original language	English (US)
Pages (from-to)	132-137
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	52
DOIs	https://doi.org/10.1016/j.ifacol.2019.08.023
State	Published - Jun 1 2019
Event	3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2019 - Oaxaca, Mexico Duration: May 20 2019 → May 24 2019

Keywords

Convex
Distributed Parameter Systems
LMI
PDE

ASJC Scopus subject areas

Control and Systems Engineering

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10.1016/j.ifacol.2019.08.023

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title = "Discussion paper: A new mathematical framework for representation and analysis of coupled PDEs",

abstract = "We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichlet, Neuman and mixed boundary conditions. The results in this paper apply to systems with a single spatial variable. We exploit a new concept of state for PDE systems which allows us to include the boundary conditions directly in the dynamics of the PDE. The resulting algorithms are implemented in Matlab, tested on several motivating and illustrative examples, and the codes have been posted online. Numerical testing indicates the approach has little or no conservatism for a large class of systems and can analyze systems of up to 20 coupled PDEs.",

keywords = "Convex, Distributed Parameter Systems, LMI, PDE",

author = "Peet, {Matthew M.} and Sachin Shivakumar and Amritam Das and Seip Weiland",

note = "Publisher Copyright: {\textcopyright} 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.; 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2019 ; Conference date: 20-05-2019 Through 24-05-2019",

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doi = "10.1016/j.ifacol.2019.08.023",

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T2 - 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2019

AU - Peet, Matthew M.

AU - Shivakumar, Sachin

AU - Das, Amritam

AU - Weiland, Seip

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichlet, Neuman and mixed boundary conditions. The results in this paper apply to systems with a single spatial variable. We exploit a new concept of state for PDE systems which allows us to include the boundary conditions directly in the dynamics of the PDE. The resulting algorithms are implemented in Matlab, tested on several motivating and illustrative examples, and the codes have been posted online. Numerical testing indicates the approach has little or no conservatism for a large class of systems and can analyze systems of up to 20 coupled PDEs.

AB - We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichlet, Neuman and mixed boundary conditions. The results in this paper apply to systems with a single spatial variable. We exploit a new concept of state for PDE systems which allows us to include the boundary conditions directly in the dynamics of the PDE. The resulting algorithms are implemented in Matlab, tested on several motivating and illustrative examples, and the codes have been posted online. Numerical testing indicates the approach has little or no conservatism for a large class of systems and can analyze systems of up to 20 coupled PDEs.

KW - Convex

KW - Distributed Parameter Systems

KW - LMI

KW - PDE

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JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

Y2 - 20 May 2019 through 24 May 2019

ER -

Discussion paper: A new mathematical framework for representation and analysis of coupled PDEs

Abstract

Keywords

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