  Sensor and actuator selection problems (SASP) are some of the core problems
in dynamic systems design and control. These problems correspond to determining
the optimal selection of sensors (measurements) or actuators (control nodes)
such that certain estimation/control objectives can be achieved. While the
literature on SASP is indeed inveterate, the vast majority of the work focuses
on linear(ized) representation of the network dynamics, resulting in the
placements of sensors or actuators (SA) that are valid for confined operating
regions. As an alternative, herein we propose a new general framework for
addressing SASP in nonlinear dynamic systems (NDS), assuming that the inputs
and outputs are linearly coupled with the nonlinear dynamics. This is
investigated through (i) classifying and parameterizing the NDS into various
nonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations,
and (iii) designing a new customized branch-and-bound (BnB) algorithm that
exploits problem structure of the SASP. The newly designed BnB routines are
computationally more attractive than the standard one and also directly
applicable to solve SASP for linear systems. In contrast with contemporary
approaches from the literature, our approach is suitable for finding the
optimal SA combination for stable/unstable NDS that ensures stabilization of
estimation error and closed-loop dynamics through a simple linear feedback
control policy.
