This is a continuation of our Northeastern ECE PhD Student Seminar Series (NEPSSS). You can find more information about the series on the NEPSSS page here.
--- Talk #1 ---
Title: Positive Stabilization With Maximum Stability Radius for Continuous-Time Dynamic Systems
Speaker: AmirReza Oghbaee
Abstract: Positive systems have attracted much attention nowadays due to their numerous applications in modeling and control of physical, biological and economical systems. The state trajectory of such system remains in the nonnegative quadrant of the state space for any given nonnegative initial condition. This class of systems have nice stability and robustness properties. One can take advantage of these interesting properties to robustly stabilize general dynamic systems such that the closed-loop system becomes positive. One of the most important measures in robust control analysis is stability radius. This measure provides the amount of uncertainty that system can cope with before it becomes unstable. There are two types of stability radius defined; complex and real stability radius. Computation of real stability radius is more involved than its complex counterpart. Although the complex and real stability radius are different for a general LTI system, it has been found that they are equal for the class of positive system. In fact, a closed form expression can be obtained to find the stability radius of positive system. In this research, we try to positively stabilize a general uncertain system with the constraint of maximizing stability radius by using a state feedback control law. The necessary and sufficient conditions for the existence of controllers satisfying the positivity constraints are provided. This constrained stabilization problem will be formulated and solved using linear programming (LP) and linear matrix inequality (LMI). With the aid of bounded real lemma, the major contribution is to solve the constrained positive stabilization with maximum stability radius for both regular and time-delay systems.
--- Talk #2 ---
Title: A Sparse Nonnegative Demixing Algorithm with Intrinsic Regularization for Multiplexed Fluorescence Tomography
Speaker: Vivan Pera
Abstract: Fluorescence molecular tomography (FMT) is an optical technique that uses near-infrared light to perform quantitative, three-dimensional imaging of fluorophores in whole animals noninvasively. It is becoming an important tool in preclinical imaging of small animals and has been employed to image tumors and assess response to anti-cancer therapeutics. However, the inability to perform high-throughput imaging of multiple fluorescent targets (“multiplexing”) in bulk tissue remains a limitation. Recent work in our group suggests that joint measurement of spectral and temporal fluorophore data can enable robust identification (“demixing”) and localization of at least four concurrent fluorophores. Here we present a novel demixing strategy for this data, which incorporates ideas from sparse subspace clustering and compressed sensing. We will review the basic principles of FMT, present our demixing algorithm, and quantify its performance.
Faculty advisors: Dana Brooks and Mark Niedre