arXiv subjects

Solmaz S. Kia

Publications and source records attributed to Solmaz S. Kia.

41 records · Page 3Linked to original sources

arXiv2017

Cycle flow formulation of optimal network flow problems for centralized and decentralized solvers

When the underlying physical network layer in optimal network flow problems is a large graph, the associated optimization problem has a large set of decision variables. In this paper, we discuss how the cycle basis from graph theory can be used to reduce the size of this decision variable space. The idea is to eliminate the aggregated flow conservation constraint of these problems by explicitly characterizing its solutions in terms of the span of the columns of the transpose of a fundamental cycle basis matrix of the network plus a particular solution. We show that for any given input/output flow vector, a particular solution can be efficiently constructed from tracing any path that connects a source node to a sink node. We demonstrate our results over a minimum cost flow problem as well as an optimal power flow problem with storage and generation at the nodes. We also show that the new formulation of the minimum cost flow problem based on the cycle basis variables is amenable to a distributed solution. In this regard, we apply our method over a distributed alternating direction method of multipliers (ADMM) solution and demonstrate it over a numerical example.

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arXiv2015

Cooperative localization for mobile agents: a recursive decentralized algorithm based on Kalman filter decoupling

We consider cooperative localization technique for mobile agents with communication and computation capabilities. We start by provide and overview of different decentralization strategies in the literature, with special focus on how these algorithms maintain an account of intrinsic correlations between state estimate of team members. Then, we present a novel decentralized cooperative localization algorithm that is a decentralized implementation of a centralized Extended Kalman Filter for cooperative localization. In this algorithm, instead of propagating cross-covariance terms, each agent propagates new intermediate local variables that can be used in an update stage to create the required propagated cross-covariance terms. Whenever there is a relative measurement in the network, the algorithm declares the agent making this measurement as the interim master. By acquiring information from the interim landmark, the agent the relative measurement is taken from, the interim master can calculate and broadcast a set of intermediate variables which each robot can then use to update its estimates to match that of a centralized Extended Kalman Filter for cooperative localization. Once an update is done, no further communication is needed until the next relative measurement.

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arXiv2015

Distributed event-triggered communication for dynamic average consensus in networked systems

This paper presents distributed algorithmic solutions that employ opportunistic inter-agent communication to achieve dynamic average consensus. In our solutions each agent is endowed with a local criterion that enables it to determine whether to broadcast its state to its neighbors. Our starting point is a continuous-time distributed coordination strategy that, under continuous-time communication, achieves practical asymptotic tracking of the dynamic average of the time-varying agents' reference inputs. Then, for this algorithm, depending on the directed or undirected nature of the time-varying interactions and under suitable connectivity conditions, we propose two different distributed event-triggered communication laws that prescribe agent communications at discrete time instants in an opportunistic fashion. In both cases, we establish positive lower bounds on the inter-event times of each agent and characterize their dependence on the algorithm design parameters. This analysis allows us to rule out the presence of Zeno behavior and characterize the asymptotic correctness of the resulting implementations. Several simulations illustrate the results.

math.OC↗

arXiv2014

Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithm's correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results.

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arXiv2014

Dynamic Average Consensus under Limited Control Authority and Privacy Requirements

This paper introduces a novel continuous-time dynamic average consensus algorithm for networks whose interaction is described by a strongly connected and weight-balanced directed graph. The proposed distributed algorithm allows agents to track the average of their dynamic inputs with some steady-state error whose size can be controlled using a design parameter. This steady-state error vanishes for special classes of input signals. We analyze the asymptotic correctness of the algorithm under time-varying interaction topologies and characterize the requirements on the stepsize for discrete-time implementations. We show that our algorithm naturally preserves the privacy of the local input of each agent. Building on this analysis, we synthesize an extension of the algorithm that allows individual agents to control their own rate of convergence towards agreement and handle saturation bounds on the driving command. Finally, we show that the proposed extension additionally preserves the privacy of the transient response of the agreement states and the final agreement value from internal and external adversaries. Numerical examples illustrate the results.

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