  The problem of placing or selecting sensors and control nodes plays a pivotal
role in the operation of dynamic networks. This paper proposes optimal
algorithms and heuristics to solve the simultaneous sensor and actuator
selection problem in linear dynamic networks. In particular, a sufficiency
condition of static output feedback stabilizability is used to obtain the
minimal set of sensors and control nodes needed to stabilize an unstable
network. We show the joint sensor/actuator selection and output feedback
control can be written as a mixed-integer nonconvex problem. To solve this
nonconvex combinatorial problem, three methods based on (1) mixed-integer
nonlinear programming, (2) binary search algorithms, and (3) simple heuristics
are proposed. The first method yields optimal solutions to the selection
problem---given that some constants are appropriately selected. The second
method requires a database of binary sensor/actuator combinations, returns
optimal solutions, and necessitates no tuning parameters. The third approach is
a heuristic that yields suboptimal solutions but is computationally attractive.
The theoretical properties of these methods are discussed and numerical tests
on dynamic networks showcase the trade-off between optimality and computational
time.
