Optimization and Inference in Networked Dynamical Systems: A Control Theoretic Approach
Saadatniaki, Fakhteh.
2019
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In this thesis, we
study problems in the modeling, analysis, and design of complex, distributed, and
networked dynamical systems. More specifically, we investigate three distinct problems
in networked systems and control theory as follows: We first address a problem in
distributed estimation where a network of agents is tasked to estimate the state of a
Continuous-Time, Linear Time-Invariant ... read moresystem under the assumption that no agent
possesses enough measurements in its communication range to estimate the entire system
state on its own. In this context, we provide a networked Kalman-type estimator that
combines prediction and innovation with information fusion among the agents and consider
an approach based on designing static estimator gains. The main contribution of this
work is to analyze the estimation error using the notions of dissipativity and the
input-output approach, enabling us to formulate stability and performance arguments as
quasiconvex optimization problems involving linear matrix inequalities. We show that the
resulting estimation error is stable and further ensures a given level of performance
regarding noise rejection. Next, we study the optimal control of information epidemics
and characterize a variant of the viral marketing phenomenon over heterogeneous social
networks. The marketing objective investigated in this framework is product adoption. In
this context, borrowing concepts from the theory of epidemic processes, we model the
transitions of the members of the target market between different stages of the adoption
process; specifically, we introduce a simple yet insightful 3-compartment setup, i.e.,
the potential-adopting-dormant-potential model. We then propose an optimal control
scheme aiming at simultaneously optimizing the population of the adopting and dormant
compartments under given time and resource constraints. We prove the existence of the
solution to the optimal control problem and provide both analytical and numerical
solutions using the Pontryagin Maximum Principle and Forward-Backward Sweep Method,
respectively. Finally, motivated by various applications from large-scale data science
to mobile wireless sensor networks, we aim to solve the distributed optimization problem
over multi-agent networks, where each agent has a local function derived from private
information. The goal is to have agents collaborate with each other to optimize the sum
of these local functions. Existing algorithms mostly deal with the corresponding
problems under the assumption that the underlying network topology is
strongly-connected, static, and undirected. The contribution of this work lies in the
relaxation of such assumptions on the network topology. In particular, we assume that
agents communicate according to a time-varying directed graph and present a
computationally efficient fast distributed optimization algorithm. Contrary to the
existing work, our proposed algorithm does not require the estimation of the Perron
eigenvector of the weight matrices. Instead, the proposed approach, termed
as~TV-$\mathcal(AB)$, relies on a novel information mixing approach exploiting both row
and column-stochastic weights to achieve agreement toward the optimal solution when the
underlying graph is directed. We show that~TV-$\mathcal(AB)$ converges linearly to the
optimal solution when the global objective is smooth and strongly-convex, and the
underlying time-varying network exhibits bounded connectivity. We derive the convergence
results based on the stability analysis of a linear system of inequalities along with a
matrix perturbation argument.
Thesis (Ph.D.)--Tufts University, 2019.
Submitted to the Dept. of Electrical Engineering.
Advisor: Usman Khan.
Committee: Usman Khan, Aleksandar Stanković, Babak Moaveni, and Yousof Naderi.
Keywords: Electrical engineering, and Mathematics.read less - ID:
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