Mathematics of Computation
Representation and control of infinite dimensional systems (vol. 1)
Representation and control of infinite dimensional systems (vol. 1)
Adaptive Reduced-Order Controllers for a Thermal Flow System Using Proper Orthogonal Decomposition
SIAM Journal on Scientific Computing
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
SIAM Journal on Numerical Analysis
Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem
Computational Optimization and Applications
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Trust-region proper orthogonal decomposition for flow control
Trust-region proper orthogonal decomposition for flow control
SIAM Journal on Control and Optimization
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Modeling and control of physical processes using proper orthogonal decomposition
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Journal of Scientific Computing
State Trajectory Compression for Optimal Control with Parabolic PDEs
SIAM Journal on Scientific Computing
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The main focus of this paper is on an a-posteriori analysis for the method of proper orthogonal decomposition (POD) applied to optimal control problems governed by parabolic and elliptic PDEs. Based on a perturbation method it is deduced how far the suboptimal control, computed on the basis of the POD model, is from the (unknown) exact one. Numerical examples illustrate the realization of the proposed approach for linear-quadratic problems governed by parabolic and elliptic partial differential equations.