Minimum energy control subject to output constraints: numerical approach

The aim is to characterise the minimum energy control that steers a parabolic system to a final state between two prescribed functions only on a subregion of the evolution system domain. This problem is solved by two approaches. The first uses the Lagrangian multiplier method, and the second is based on subdifferential techniques. An algorithm is also given for the computation of the optimal control. The results are illustrated by numerical simulations which lead to some conjectures