TY - GEN
T1 - Representation of linear PDEs with spatial integral terms as Partial Integral Equations
AU - Shivakumar, Sachin
AU - Das, Amritam
AU - Peet, Matthew M.
N1 - Publisher Copyright:
© 2023 American Automatic Control Council.
PY - 2023
Y1 - 2023
N2 - In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial integral terms appearing in the dynamics and the boundary conditions. The PIE representation is obtained by performing a change of variable where every PDE state is replaced by its highest, well-defined derivative using the Fundamental Theorem of Calculus to obtain a new equation (a PIE). We show that this conversion from PDE representation to PIE representation can be written in terms of explicit maps from the PDE parameters to PIE parameters. Lastly, we present numerical examples to demonstrate the application of the PIE representation by performing stability analysis of PDEs via convex optimization methods.
AB - In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial integral terms appearing in the dynamics and the boundary conditions. The PIE representation is obtained by performing a change of variable where every PDE state is replaced by its highest, well-defined derivative using the Fundamental Theorem of Calculus to obtain a new equation (a PIE). We show that this conversion from PDE representation to PIE representation can be written in terms of explicit maps from the PDE parameters to PIE parameters. Lastly, we present numerical examples to demonstrate the application of the PIE representation by performing stability analysis of PDEs via convex optimization methods.
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U2 - 10.23919/ACC55779.2023.10156465
DO - 10.23919/ACC55779.2023.10156465
M3 - Conference contribution
AN - SCOPUS:85167837320
T3 - Proceedings of the American Control Conference
SP - 1788
EP - 1793
BT - 2023 American Control Conference, ACC 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2023 American Control Conference, ACC 2023
Y2 - 31 May 2023 through 2 June 2023
ER -