Remarks on quadratic optimal control problems in Hilbert spaces (Q788267)

In the beginning a short survey of known results in the field of quadratic optimal control problems, described by operator equations in Hilbert spaces is presented. Then, some lemmas about the existence and uniqueness of the solution of some modified quadratic problems are stated and proved. Further on, theorems about upper and lower bounds of the optimal control and the cost functional are formulated and proved. These bounds can be used for estimating how close a suboptimal control is to the optimal one without calculating the latter. Employing the bounds, for some quadratic problems a sufficient condition for the optimal control to be of bang-bang type is derived.