CAREER: Algorithms and Fundamental Limitations for Sparse Control

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The proposal is to study the design of feedback control strategies which stabilize and steer systems by affecting them in only a few variables. The motivation comes from applications which are either large-scale or geographically distributed and therefore cannot be feasibly affected in many places. A primary motivating application is the control of metabolic chemical reaction networks within the human body which can be affected by drugs typically interacting with only a few out of the tens of thousands reagents in the human metabolism. The goal is to design sparse strategies which stabilize models of metabolic networks away from undesirable equilibria with an eye to developing algorithms which could one day be used to design drugs regulating human metabolism.Intellectual Merit:The design of efficient algorithms which find the sparsest possible controllers for linear and polynomial dynamical systems will be investigated. Whenever this is not possible intractability results rigorously demonstrating this impossibility will be developed. A central focus of the work will be on computational complexity issues as the search for sparse controllers turns out to be intractable in many cases of interest. The main contribution will be in the development of algorithms which take advantage of the generic properties of real-world systems to avoid intractability barriers and efficiently find very sparse controllers.Broader Impacts:The algorithms have potential to become standard tools of control engineering practice whenever large systems are involved or when the number of sensors and actuators available is limited. The PI will work to ensure that the protocols developed here enter into the control curriculum. Both undergraduate and graduate students will be involved in the execution of the research. Outreach activities are planned, especially for beginning undergraduate students with the aim of increasing retention rates of under-represented groups in engineering.