Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
SIAM Journal on Control and Optimization
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
"Natural norm" a posteriori error estimators for reduced basis approximations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
SIAM Journal on Control and Optimization
Adaptive Finite Elements for Elliptic Optimization Problems with Control Constraints
SIAM Journal on Control and Optimization
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
SIAM Journal on Scientific Computing
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
POD a-posteriori error estimates for linear-quadratic optimal control problems
Computational Optimization and Applications
SIAM Journal on Scientific Computing
An "$hp$" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations
SIAM Journal on Scientific Computing
Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations
Mathematical and Computer Modelling: An International Journal
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We propose a Reduced Basis method for the solution of parametrized optimal control problems with control constraints for which we extend the method proposed in Dedè, L. (SIAM J. Sci. Comput. 32:997, 2010) for the unconstrained problem. The case of a linear-quadratic optimal control problem is considered with the primal equation represented by a linear parabolic partial differential equation. The standard offline---online decomposition of the Reduced Basis method is employed with the Finite Element approximation as the "truth" one for the offline step. An error estimate is derived and an heuristic indicator is proposed to evaluate the Reduced Basis error on the optimal control problem at the online step; also, the indicator is used at the offline step in a Greedy algorithm to build the Reduced Basis space. We solve numerical tests in the two-dimensional case with applications to heat conduction and environmental optimal control problems.