Boundary control of a parabolic system with distributed parameters on a graph in the class of summable functions

This paper considers a differential system whose state is described by a parabolic initial boundary value problem with distributed parameters on a graph. For the above system, the author studies the problem of boundary control in the class of generalized solutions. Control action and observations are simultaneously boundary. And finally, the existence conditions of a unique control action and the expressions characterizing control actions are obtained.