Controllability properties of fractional PDE

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

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…