Control Node and Sensor Selection in Dynamical Systems

Complex dynamical systems are comprised of many interconnected, smaller subsystems whereeach is characterized by its own dynamics, control nodes, and a set of measurements. These dynamicalsystems are governed by mean of actuators applied to the control nodes and often, in thecase where not all states are accessible, the state trajectories need be estimated by mean of measurementsobtained from the sensors. Although it is preferred to use all control nodes and sensorsto perform control, utilizing large number of control nodes and sensors is not practical and cost-effectiveespecially for large-scale dynamical systems. To that end, this dissertation is dedicated toaddress the problem of control node and/or sensor selection: the search of the best configurationof control nodes and sensors such that the overall system is controllable and/or observable whileoptimizing some user-defined metrics and satisfying some logistical constraints. Several researchobjectives are considered herein: (a) investigating the joint control node and sensor selection forstabilization via static state-feedback control approach of linear dynamical systems, (b) proposing ageneral framework to solve the control node and sensor selection for nonlinear dynamical systems,(c) introducing a unified framework to parameterize the constants characterizing the correspondingnonlinearities, (d) exploring a Gramian-based approach to place sensors in traffic networks, and(e) proposing the concept of average observability to efficiently solve the sensor selection usingGreedy algorithms.