Controllability properties for equations with memory of fractional type
Provides theoretical controllability results for a broad class of memory-based systems, clarifying limitations for exact control.
The paper studies control systems with memory, including fractional derivatives, and finds that approximate controllability is inherited from the heat equation, but exact controllability to zero only holds when the system reduces to the standard heat equation.
We study a general class of control systems with memory, which in particular includes systems with fractional derivatives and integrals and also the standard heat equation. We prove that the approximate controllability property of the heat equation is inherited by every system with memory in this class while controllability to zero is a singular property, which holds solely in the special case that the system indeed reduces to the standard heat equation.