Event
Ph.D. Dissertation Defense: Shinkyu Park
Friday, November 6, 2015
12:00 p.m.
AVW 2224
Maria Hoo
301 405 3681
mch@umd.edu
ANNOUNCEMENT: Ph.D. Dissertation Defense
Name: Shinkyu Park
Committee:
Professor Nuno Martins, Chair/Advisor
Professor P. S. Krishnaprasad
Professor Richard La
Professor Andre Tits
Professor Nikhil Chopra, Dean’s Representative
Data/time: Friday, November 6, 2015 / 12:00 PM
Location: AVW 2224
Title: Distributed Estimation and Stability of Evolutionary Games for Large Populations with Applications to Cyber Physical Systems
Abstract:
We investigate three problems: in the first we investigate distributed state estimation for linear time-invariant plants; the second studies the effect of communication costs in a two-block remote estimation problem; while in the third we examine stability of evolutionary games for large populations.
Problem 1: Consider that an autonomous linear time-invariant (LTI) plant is given and that each member of a network of LTI observers accesses a portion of the output of the plant. The dissemination of information within the network is dictated by a pre-specified directed graph in which each vertex represents an observer. This work proposes a distributed estimation scheme that is a natural generalization of consensus in which each observer computes its own state estimate using only the portion of the output vector accessible to it and the state estimates of other observers that are available to it, according to the graph. Unlike straightforward high-order solutions in which each observer broadcasts its measurements throughout the network, the average size of the state of each observer in the proposed scheme does not exceed the order of the plant plus one. We determine necessary and sufficient conditions for the existence of a parameter choice for which the proposed scheme attains asymptotic omniscience of the state of the plant at all observers. The conditions reduce to certain detectability requirements that imply that if omniscience is not possible under the proposed scheme then it is not viable under any other scheme -- including higher order LTI, nonlinear, and time-varying ones -- subject to the same graph.
Problem 2: We investigate a problem of remote state estimation for Markov processes. Consider a two-block framework in which a sensing unit accesses the full state of a Markov process and decides whether to transmit information on the state to a remotely located estimator, where each transmission incurs a communication cost. The estimator finds the best state estimate of the process using the information received from the sensing unit. The main purpose of this work is to design transmission policies and estimation rules that dictate decision making of the sensing unit and estimator, respectively, and minimize a cost functional which combines the expectation of estimation error and communication costs. Our main results establish the existence of a jointly optimal solution, and describe and analyze an iterative procedure that computes a person-by-person optimal solution.
Problem 3: We explore an energy conservation and dissipation (passivity) aspect of evolutionary dynamics in evolutionary game theory. We define a notion of passivity for evolutionary dynamics, and characterize it in connection with state-space realizations of the dynamics. Based on the characterization, we identify properties of passive evolutionary dynamics, and provide stability results for the dynamics in population games, where we establish stability in terms of dissipation of stored energy defined by passivity. In addition, we provide numerical simulations to illustrate implications of stability for passive dynamics.
