Dynamics over Signed Networks

A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two different types of interactions take place along the positive and negative links, respectively, arise from various biological, social, political, and economic systems. As modifications to the conventional DeGroot dynamics for positive links, two basic types of negative interactions along negative links, namely the opposing rule and the repelling rule, have been proposed and studied in the literature. This paper reviews a few fundamental convergence results for such dynamics over deterministic or random signed networks under a unified algebraic-graphical method. We show that a systematic tool of studying node state evolution over signed networks can be obtained utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie

Timed Automata Approach for Motion Planning Using Metric Interval Temporal Logic

In this paper, we consider the robot motion (or task) planning problem under some given time bounded high level specifications. We use metric interval temporal logic (MITL), a member of the temporal logic family, to represent the task specification and then we provide a constructive way to generate a timed automaton and methods to look for accepting runs on the automaton to find a feasible motion (or path) sequence for the robot to complete the task.Comment: Full Version for ECC 201

Value of Information in Feedback Control

In this article, we investigate the impact of information on networked control systems, and illustrate how to quantify a fundamental property of stochastic processes that can enrich our understanding about such systems. To that end, we develop a theoretical framework for the joint design of an event trigger and a controller in optimal event-triggered control. We cover two distinct information patterns: perfect information and imperfect information. In both cases, observations are available at the event trigger instantly, but are transmitted to the controller sporadically with one-step delay. For each information pattern, we characterize the optimal triggering policy and optimal control policy such that the corresponding policy profile represents a Nash equilibrium. Accordingly, we quantify the value of information $\operatorname{VoI}_k$ as the variation in the cost-to-go of the system given an observation at time $k$. Finally, we provide an algorithm for approximation of the value of information, and synthesize a closed-form suboptimal triggering policy with a performance guarantee that can readily be implemented

Real time control for NASA robotic gripper

Control laws (in some optimal sense) are being developed for the gripper/nut runner end effector. Control laws for the gripper and nut runner portions of the end effector may be developed independently since these two systems are decoupled. A hybrid force/position controller will be used for both the gripper and nut runner. The development of the gripper controller is explained. Sensory data available to the controller is obtained from an array of strain gages as well as a linear potentiometer. Applying well known optimal control theoretic principles, the control which minimizes the transition time between positions is obtained. In addition, a robust force control scheme is developed to contend with the strain gage drift caused by extreme temperature variations encountered in space

Exponentially convergent data assimilation algorithm for Navier-Stokes equations

The paper presents a new state estimation algorithm for a bilinear equation representing the Fourier- Galerkin (FG) approximation of the Navier-Stokes (NS) equations on a torus in R2. This state equation is subject to uncertain but bounded noise in the input (Kolmogorov forcing) and initial conditions, and its output is incomplete and contains bounded noise. The algorithm designs a time-dependent gain such that the estimation error converges to zero exponentially. The sufficient condition for the existence of the gain are formulated in the form of algebraic Riccati equations. To demonstrate the results we apply the proposed algorithm to the reconstruction a chaotic fluid flow from incomplete and noisy data

Selfish Response to Epidemic Propagation

An epidemic spreading in a network calls for a decision on the part of the network members: They should decide whether to protect themselves or not. Their decision depends on the trade-off between their perceived risk of being infected and the cost of being protected. The network members can make decisions repeatedly, based on information that they receive about the changing infection level in the network. We study the equilibrium states reached by a network whose members increase (resp. decrease) their security deployment when learning that the network infection is widespread (resp. limited). Our main finding is that the equilibrium level of infection increases as the learning rate of the members increases. We confirm this result in three scenarios for the behavior of the members: strictly rational cost minimizers, not strictly rational, and strictly rational but split into two response classes. In the first two cases, we completely characterize the stability and the domains of attraction of the equilibrium points, even though the first case leads to a differential inclusion. We validate our conclusions with simulations on human mobility traces.Comment: 19 pages, 5 figures, submitted to the IEEE Transactions on Automatic Contro