Abstract-In this paper, we study structural controllability of a linear time invariant (LTI) composite system consisting of several subsystems. We assume that the neighbourhood of each subsystem is unconstrained, i.e., any subsystem can interact with any other subsystem. The interaction links between subsystems are referred as interconnections. We assume the composite system to be structurally controllable if all possible interconnections are present, and our objective is to identify the minimum set of interconnections required to keep the system structurally controllable. We consider structurally identical subsystems, i.e., the zero/non-zero pattern of the state matrices of the subsystems are the same, but dynamics can be different. We present a polynomial time optimal algorithm to identify the minimum cardinality set of interconnections that subsystems must establish to make the composite system structurally controllable. Our general result we apply to special cases, where the minimum number can be more directly obtained. We considered controller canonical form, so-called structurally cyclic systems and subsystems that are structurally controllable with a single input. The minimum number of interconnections required depends on some indices we defined in the paper, maximum commonality index, α N , and unique dilation index, β I . More connectedness of subsystems leads to lower total value of α N + β I and if the subsystems have fewer number of connected components α N decreases.
Paper REF considered the unconstrained case of the optimal constrained network topology design problem when the subsystems are heterogeneous and gave a polynomial-time algorithm.
Optimal Selection of Interconnections in Composite Systems for Structural Controllability
arXiv: Optimization and Control
Mathematics