A problem in control of elastodynamics with piezoelectric effects
Abstract
We consider an optimal control problem where the state equations are a coupled hyperbolic–elliptic system. This system arises in elastodynamics with piezoelectric effects—the elastic stress tensor is a function of elastic displacement and electric potential. The electric flux acts as the control variable and bound constraints on the control are considered. We develop a complete analysis for the state equations and the control problem. The requisite regularity on the control, to show the well-posedness of the state equations, is enforced using the cost functional. We rigorously derive the first-order necessary and sufficient conditions using adjoint equations and further study their well-posedness. For spatially discrete (time-continuous) problems, we show the convergence of our numerical scheme. Three-dimensional numerical experiments are provided showing convergence properties of a fully discrete method and the practical applicability of our approach.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 23, 2019
- Source ID
- 10.1093/imanum/drz047
Entities
People
- Francisco-javier Sayas
- Harbir Antil
- Thomas S Brown
Organizations
- Air Force Office of Scientific Research
- George Mason University
- National Science Foundation
- University of Delaware