Optimal synthesis control for evolution equations subject to nonlocal inputs

Abstract: 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 a perspective akin to the one taken in our previous research work on the LQ problem for integro-differential equations — which combines a variational approach to the minimization problem with the consideration of a suitably enlarged state space — we offer a full (closed-loop, Riccati-based) solution to the optimization problem.