r-Robustness and (r,s)-Robustness of Circulant Graphs

There has been recent growing interest in graph theoretical properties known as r- and (r,s)-robustness. These properties serve as sufficient conditions guaranteeing the success of certain consensus algorithms in networks with misbehaving agents present. Due to the complexity of determining the robustness for an arbitrary graph, several methods have previously been proposed for identifying the robustness of specific classes of graphs or constructing graphs with specified robustness levels. The majority of such approaches have focused on undirected graphs. In this paper we identify a class of scalable directed graphs whose edge set is determined by a parameter k and prove that the robustness of these graphs is also determined by k. We support our results through computer simulations.Comment: 6 pages, 6 figures. Accepted to 2017 IEEE CD

Finite-Time Resilient Formation Control with Bounded Inputs

In this paper we consider the problem of a multi-agent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents can converge to a formation with respect to a set of leaders. The controller employs a norm-based filtering mechanism, and unlike most prior algorithms, also incorporates input bounds. In addition, the controller is shown to guarantee convergence in finite time. A sufficient condition for the controller to guarantee convergence is shown to be a graph theoretical structure which we denote as Resilient Directed Acyclic Graph (RDAG). Further, we employ our filtering mechanism on a discrete time system which is shown to have exponential convergence. Our results are demonstrated through simulations

Advancements in Adversarially-Resilient Consensus and Safety-Critical Control for Multi-Agent Networks

The capabilities of and demand for complex autonomous multi-agent systems, including networks of unmanned aerial vehicles and mobile robots, are rapidly increasing in both research and industry settings. As the size and complexity of these systems increase, dealing with faults and failures becomes a crucial element that must be accounted for when performing control design. In addition, the last decade has witnessed an ever-accelerating proliferation of adversarial attacks on cyber-physical systems across the globe. In response to these challenges, recent years have seen an increased focus on resilience of multi-agent systems to faults and adversarial attacks. Broadly speaking, resilience refers to the ability of a system to accomplish control or performance objectives despite the presence of faults or attacks. Ensuring the resilience of cyber-physical systems is an interdisciplinary endeavor that can be tackled using a variety of methodologies. This dissertation approaches the resilience of such systems from a control-theoretic viewpoint and presents several novel advancements in resilient control methodologies. First, advancements in resilient consensus techniques are presented that allow normally-behaving agents to achieve state agreement in the presence of adversarial misinformation. Second, graph theoretic tools for constructing and analyzing the resilience of multi-agent networks are derived. Third, a method for resilient broadcasting vector-valued information from a set of leaders to a set of followers in the presence of adversarial misinformation is presented, and these results are applied to the problem of propagating entire knowledge of time-varying Bezier-curve-based trajectories from leaders to followers. Finally, novel results are presented for guaranteeing safety preservation of heterogeneous control-affine multi-agent systems with sampled-data dynamics in the presence of adversarial agents.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168102/1/usevitch_1.pd

Insulin, Glucose, and β-cell Diffusion Analysis

The purpose of this project is to further understand the function of extruded polytetrafluoroethylene (ePTFE) membranes in the pursuit of creating an implantable, removable pancreas device. This device would be filled with pancreas cells and automatically regulate blood sugar for patients with diabetes. Dr. Alonzo Cook’s lab is currently pursuing understanding the process of taking a patient’s own cells, reprogramming them into stem cells, and then differentiating them into pancreas cells. The device that is the end goal of this project is the main foreseen use of these differentiated pancreas cells. This project focuses on studying how essential nutrients diffuse through the ePTFE membrane as well as whether the cells themselves can migrate across