## Controllability properties of fractional PDE

Controllability properties of fractional PDE By Umberto Biccari   Controllability of the fractional heat equation Let be an open and nonempty subset. Consider the following non-local one-dimensional heat equation defined on the domain where is a given initial datum. In (1), for all , denotes the one-dimensional fractional Laplace operator, which is defined as the following singular integral Here, is…

## Stochastic optimization for simultaneous control

Stochastic optimization for simultaneous control By Umberto Biccari   What is a simultaneous control problem? Consider the following parameter-dependent linear control system with The matrix is associated with the Brunovsky canonical form of the linear ODE where denotes the -th derivative of the function .   In (1)-(2), , , denotes the state, the matrix describes the dynamics, and the…