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Sensor and actuator selection problems (SASP) are some of the core problemsin dynamic systems design and control. These problems correspond to determiningthe optimal selection of sensors (measurements) or actuators (control nodes)such that certain estimation/control objectives can be achieved. While theliterature on SASP is indeed inveterate, the vast majority of the work focuseson linear(ized) representation of the network dynamics, resulting in theplacements of sensors or actuators (SA) that are valid for confined operatingregions. As an alternative, herein we propose a new general framework foraddressing SASP in nonlinear dynamic systems (NDS), assuming that the inputsand outputs are linearly coupled with the nonlinear dynamics. This isinvestigated through (i) classifying and parameterizing the NDS into variousnonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations,and (iii) designing a new customized branch-and-bound (BnB) algorithm thatexploits problem structure of the SASP. The newly designed BnB routines arecomputationally more attractive than the standard one and also directlyapplicable to solve SASP for linear systems. In contrast with contemporaryapproaches from the literature, our approach is suitable for finding theoptimal SA combination for stable/unstable NDS that ensures stabilization ofestimation error and closed-loop dynamics through a simple linear feedbackcontrol policy.

Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound