Dynamic optimization of dissipative PDE systems using nonlinear order reduction

Antonios Armaou, Panagiotis D. Christofides

Research output: Contribution to journalConference article

2 Citations (Scopus)

Abstract

In this work, we propose a computationally efficient method for the solution of dynamic constraint optimization problems arising in the context of spatially-distributed processes governed by highly-dissipative non-linear partial differential equations (PDEs). The method is based on spatial discretization using combination of the method of weighted residuals with spatially-global basis functions and approximate inertial manifolds. We use the Kuramoto-Sivashinsky equation, a model that describes incipient instabilities in a variety of physical and chemical systems, to demonstrate the implementation and evaluate the effectiveness of the proposed optimization method.

Original languageEnglish (US)
Pages (from-to)2310-2316
Number of pages7
JournalProceedings of the IEEE Conference on Decision and Control
Volume2
StatePublished - Dec 1 2002
Event41st IEEE Conference on Decision and Control - Las Vegas, NV, United States
Duration: Dec 10 2002Dec 13 2002

Fingerprint

Order Reduction
Dynamic Optimization
Partial differential equations
Nonlinear systems
Partial differential equation
Nonlinear Systems
Approximate Inertial Manifolds
Kuramoto-Sivashinsky Equation
Nonlinear Partial Differential Equations
Optimization Methods
Basis Functions
Discretization
Optimization Problem
Evaluate
Demonstrate
Model

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

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Dynamic optimization of dissipative PDE systems using nonlinear order reduction. / Armaou, Antonios; Christofides, Panagiotis D.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2, 01.12.2002, p. 2310-2316.

Research output: Contribution to journalConference article

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AU - Christofides, Panagiotis D.

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AB - In this work, we propose a computationally efficient method for the solution of dynamic constraint optimization problems arising in the context of spatially-distributed processes governed by highly-dissipative non-linear partial differential equations (PDEs). The method is based on spatial discretization using combination of the method of weighted residuals with spatially-global basis functions and approximate inertial manifolds. We use the Kuramoto-Sivashinsky equation, a model that describes incipient instabilities in a variety of physical and chemical systems, to demonstrate the implementation and evaluate the effectiveness of the proposed optimization method.

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