Work

Extension of the Partial Integral Equation Representation to GPDE Input–Output Systems

Year: 2024

Type: article

Abstract: Partial integral equation (PIE) representation of a partial differential equation (PDE) allows using computationally tractable algorithms for analysis, simulation, and optimal control. However, the PIE representation has not previously been extended to many of the complex, higher order PDEs that may be encountered in speculative or data-based models. In this article, we propose PIE representations for a large class of such PDE models, including higher order derivatives, boundary-valued inputs, and coupling with ordinary differential equations. The main technical contribution that enables this extension is a generalization of Cauchy's rule for repeated integration. The process of conversion of a complex PDE model to a PIE is simplified through a PDE modeling interface in the open-source software PIETOOLS. Numerical tests and illustrations are used to demonstrate the controller synthesis and simulation of PDEs.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2024.3505954

Authors: Sachin Shivakumar, Amritam Das, Siep Weiland, Matthew Peet

Institutions: Iowa State University, Eindhoven University of Technology, Arizona State University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation

Awards: War on Boundary Conditions - A Control-Oriented Framework for Partial Differential Equations, CPS: Small: A Convex Framework for Control of Interconnected Systems over Delayed Networks, Collaborative Research: Robust Control of Large-Scale Networks with Variable Delays using Partial Integral Equations