Time optimal control for a class of evolutionary equations with applications (Q6569357)

The authors study a system that is governed by an evolutionary equation involving two linear operators and a bilinear operator. They investigate a problem of optimal control where the aim is to quickly reach a \(\sigma\)-neighbourhood of a given target point with a given radius \(\sigma\). It is not required to reach the target point exactly. In addition to the required steering time, the objective functional also contains a regularization term (control cost). The authors study the existence and uniqueness of optimal controls and several optimality conditions for the optimal control problem. The main results are applied to a class of quasistatic frictional contact problems.