DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click
HERE to register or log in.
Accession Number:
ADA280142
Title:
Finite Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems
Descriptive Note:
Contractor rept.
Corporate Author:
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
Report Date:
1994-03-01
Pagination or Media Count:
50.0
Abstract:
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows. Optimal control, Nonlinear partial differential equations, Finite dimensional approximation, Finite element methods, Von Karman equations, Ginzburg-Landau equations, Navier-Stokes equations.
Distribution Statement:
APPROVED FOR PUBLIC RELEASE
