Greedy control represents a new notion in the control theory, applicable to parameter dependent systems. The idea is to identify the most distinguished parameter values so to provide the best possible approximations of all parameter-depending controls. In such a way one avoids construction of a control function from scratch for each new parameter value, which for large systems, although feasible by the uniform controllability assumption, is time and computationally expensive.
Our analysis is based on previous work on greedy and weak greedy algorithms for parameter-depending PDEs, which we adjust to the control theory. The algorithm consists of (a possible expensive) offline part devoted to the selection of parameter representatives and the online one enabling a fast computation of an approximative control for a given parameter value within a given accuracy.
Numerical examples for system of ODEs derived by discretization of the wave/heat equation will be presented.
This work has been developed in collaboration with E. Zuazua during my stay at BCAM, Bilbao this year.
