Control of Periodic Systems Governed by Partial Differential Equations Using Averaging

As a perturbation method, averaging is a mathematical tool for dynamic analysis of time-periodic and space-periodic dynamical systems, including those governed by partial differential equations. The control design procedure presented in this work uses averaging techniques, the well-developed linear control strategies, and finite element methods. The controller is designed based on the linear averaged dynamics of a time- or space-periodic system. The controller is then used for trajectory tracking or stabilization of the periodic system. The applicability and performance of the suggested method depend on different physical parameters of the periodic system and the control parameters of the controller. The effects of these parameters are discussed in this work. Numerical simulations show acceptable performance of the proposed control design strategy for two linear and nonlinear time- and space-periodic systems, namely, the one-dimensional heat equation and the Chafee-Infante equation with periodic coefficients.

Name thesis:degree_name

M.S.

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2023

Author dc:creator

• Tahmasian, Sevak

Chair dc:contributor.committeechair

• Borggaard, Jeffrey T.

Committee members dc:contributor.committeemember

• Abaid, Nicole
• Staples, Anne E.

• Periodic systems
• averaging
• homogenization
• heat equation
• Chafee-Infante equation
• control of partial differential equations

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10919/116574

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/116574