Time optimal sampled-data controls for the heat equation (Q1690937)

The authors formulate a time-optimal sampled data control problem for parabolic equations. A starting point is to define \(L_2\) approximate null controllability for the sampled data controlled heat equation. Basing on this definition the authors find some error estimates between solutions of time optimal control and sampled data time optimal control problems. Existence and uniqueness of time optimal control problems is also discussed. The authors find that while there exists a unique optimal time control there may exist infinitely many optimal sampled data controls. Nevertheless one may chose the optimal control with the minimal norm that is unique. Thus the main idea proposed in the paper is to replace continuous-time optimal controls for heat equations by their sampled-data approximations with the minimal norm. Unfortunately, the paper is very difficult to read and contains a number of unclear sentences starting from its abstract.