Optimal control problem for unbounded bilinear systems and applications

In this paper, we will investigate the optimal control problem for unbounded bilinear systems, with (p, q)-admissible control operators. We will first study the case of finite time-horizon with unconstrained or constrained endpoint. This result is further applied to build the optimal control for infinite time horizon. Finally, we solve the bilinear optimal control for the transport equation. Then we consider the fractional diffusion equation, for which we prove the strong stabilisation by an optimal time-varying feedback control.