Reduced basis method and error estimation for parametrized optimal control problems with control constraints

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.


Published in:
Journal of Scientific Computing, 50, 2, 287-305
Year:
2012
Publisher:
Springer Verlag
ISSN:
0885-7474
Keywords:
Laboratories:




 Record created 2012-07-30, last modified 2018-03-17


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