Feedback Modal Control of Partial Differential Equations

For hybrid systems in which control consists of selection from a discrete finite set of modes, a somewhat unfamiliar formulation is needed for analysis of the possibility of closed loop (feedback) control. We are here concerned to examine the desiderata for such feedback from the viewpoint of descriptive modeling of implementation in a PDE context. A principal result is global existence, in an appropriate sense, for the implemented closed loop control system. A problem of transport on a graph is then presented to show how the relevant hypotheses might be satisfied in a PDE example.