Cherry-Picking Control Nodes and Sensors in Dynamic Networks: Mixed-Integer Nonlinear Programming Formulations, Heuristics, Applications, and Challenges
Abstract: A defining feature of dynamic networks is the prevalence of large number of real-time sensors and controllers (SaCs): sensors sampling physical data in real time and controllers driving networks to stable physical state. For example, water quality sensors measure contamination and microbial levels in drink water networks. This data is then used to determine immediate actions of controllers, such as decontaminant injections or valves flushing out contaminated water. Other dynamic networks such as energy systems and transportation networks operate in a similar fashion; they all obtain data from sensors and subsequently compute optimal signals for control nodes to follow.
Systems theory studies addressed a plethora of problems that explore optimal sensing and control algorithms. These studies, however, have three major limitations:
- The combinatorial selection of SaCs given the real-time network dynamics and uncertainty is often ignored: all SaCs are activated, resulting in higher costs and oversampling.
- The network topology is often static; that is, the selection of SaCs does not consider evolving network structure.
- The coupling between SaCs selection is rarely addressed, resulting in suboptimal SaC selection.
In this talk, the problem of simultaneously selecting SaCs in dynamic networks is formulated. The main objective is to minimize a weighted number of activated SaCs, subject to network stability and SaC logistic constraints. The problem formulation, which can be extended to perturbed nonlinear dynamic networks and time-varying selection of SaCs, entails solving a large-scale, mixed-integer nonconvex program. To address the computational complexity, convex approximations and relaxation are explored. Heuristics that are based on efficient numerical computations are also presented. The talk also sheds the light on some open research problems and challenges. Finally, applications in water networks and energy systems are illustrated.