Optimal synthesis control for evolution equations subject to nonlocal inputs

We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following the perspective taken in our previous research work on the LQ problem for integro-differential equations, where the memory term – here involving the control actions – is seen as a component of the state, we offer a full (closed-loop, Riccati-like) solution to the optimization problem.