arXiv subjects

Sonia Martinez

Publications and source records attributed to Sonia Martinez.

At least 55 records · Page 3Linked to original sources

arXiv2017

Scheduled-Asynchronous Distributed Algorithm for Optimal Power Flow

Optimal power flow (OPF) problems are non-convex and large-scale optimization problems with important applications in power networks. This paper proposes the scheduled-asynchronous algorithm to solve a distributed semidefinite programming (SDP) formulation of the OPF problem. In this formulation, every agent seeks to solve a local optimization with its own cost function, physical constraints on its nodal power injection, voltage, and power flow of the lines it is connected to, and decision constraints on variables shared with neighbors to ensure consistency of the obtained solution. In the scheduled-asynchronous algorithm, every pair of connected nodes in the electrical network update their local variables in an alternating fashion. This strategy is asynchronous, in the sense that no clock synchronization is required, and relies on an orientation of the electrical network that prescribes the precise ordering of node updates. We establish the asymptotic convergence properties to the primal-dual optimizer when the orientation is acyclic. Given the dependence of the convergence rate on the network orientation, we also develop a distributed graph coloring algorithm that finds an orientation with diameter at most five for electrical networks with geometric degree distribution. Simulations illustrate our results on various IEEE bus test cases.

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arXiv2017

Weight Design of Distributed Approximate Newton Algorithms for Constrained Optimization

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a novel Distributed Approx-Newton algorithm that approximates the standard Newton optimization method. A main property of this distributed algorithm is that it only requires agents to exchange constant-size communication messages. The convergence of this algorithm is discussed and rigorously analyzed. In addition, we aim to address the problem of designing communication topologies and weightings that are optimal for second-order methods. To this end, we propose an effective approximation which is loosely based on completing the square to address the NP-hard bilinear optimization involved in the design. Simulations demonstrate that our proposed weight design applied to the Distributed Approx-Newton algorithm has a superior convergence property compared to existing weighted and distributed first-order gradient descent methods.

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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.

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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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arXiv2013

On the performance analysis of resilient networked control systems under replay attacks

This paper studies a resilient control problem for discrete-time, linear time-invariant systems subject to state and input constraints. State measurements and control commands are transmitted over a communication network and could be corrupted by adversaries. In particular, we consider the replay attackers who maliciously repeat the messages sent from the operator to the actuator. We propose a variation of the receding-horizon control law to deal with the replay attacks and analyze the resulting system performance degradation. A class of competitive (resp. cooperative) resource allocation problems for resilient networked control systems is also investigated.

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arXiv2012

An approximate dual subgradient algorithm for multi-agent non-convex optimization

We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In contrast to previous work, we do not require that the objective, constraint functions, and state constraint sets to be convex. In order to deal with time-varying network topologies satisfying a standard connectivity assumption, we resort to consensus algorithm techniques and the Lagrangian duality method. We slightly relax the requirement of exact consensus, and propose a distributed approximate dual subgradient algorithm to enable agents to asymptotically converge to a pair of primal-dual solutions to an approximate problem. To guarantee convergence, we assume that the Slater's condition is satisfied and the optimal solution set of the dual limit is singleton. We implement our algorithm over a source localization problem and compare the performance with existing algorithms.

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arXiv2012

Storage Size Determination for Grid-Connected Photovoltaic Systems

In this paper, we study the problem of determining the size of battery storage used in grid-connected photovoltaic (PV) systems. In our setting, electricity is generated from PV and is used to supply the demand from loads. Excess electricity generated from the PV can be stored in a battery to be used later on, and electricity must be purchased from the electric grid if the PV generation and battery discharging cannot meet the demand. Due to the time-of-use electricity pricing, electricity can also be purchased from the grid when the price is low, and be sold back to the grid when the price is high. The objective is to minimize the cost associated with purchasing from (or selling back to) the electric grid and the battery capacity loss while at the same time satisfying the load and reducing the peak electricity purchase from the grid. Essentially, the objective function depends on the chosen battery size. We want to find a unique critical value (denoted as $C_{ref}^c$) of the battery size such that the total cost remains the same if the battery size is larger than or equal to $C_{ref}^c$, and the cost is strictly larger if the battery size is smaller than $C_{ref}^c$. We obtain a criterion for evaluating the economic value of batteries compared to purchasing electricity from the grid, propose lower and upper bounds on $C_{ref}^c$, and introduce an efficient algorithm for calculating its value; these results are validated via simulations.

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arXiv2011

Energy-Based Voronoi Partition in Constant Flow Environments

As is well known, energy cost can greatly impact the deployment of battery-powered sensor networks in remote environments such as rivers or oceans. Motivated by this, we propose here an energy-based metric and associate energy-based Voronoi partitions with mobile vehicles in constant flows. The metric corresponds to the minimum energy that a vehicle requires to move from one point to another in the flow environment, and the resulting partition can be used by the vehicles in cooperative control tasks such as task assignment and coverage. Based on disk-based and asymptote-based approximations of the Voronoi regions, we determine a subset (or lower bound) and superset (or upper bound) of an agent's Voronoi neighbors. We then show that, via simulations, the upper bound is tight and its cardinality remains bounded as the number of generators increases. Finally, we propose efficient algorithms to compute the upper bound (especially when the generators dynamically change), which enables the fast calculation of Voronoi regions.

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arXiv2011

On distributed convex optimization under inequality and equality constraints via primal-dual subgradient methods

We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set. The objective function is defined by a sum of local objective functions, while the global constraint set is produced by the intersection of local constraint sets. In particular, we study two cases: one where the equality constraint is absent, and the other where the local constraint sets are identical. We devise two distributed primal-dual subgradient algorithms which are based on the characterization of the primal-dual optimal solutions as the saddle points of the Lagrangian and penalty functions. These algorithms can be implemented over networks with changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the Slater's condition.

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arXiv2010

On the convergence time of asynchronous distributed quantized averaging algorithms

We come up with a class of distributed quantized averaging algorithms on asynchronous communication networks with fixed, switching and random topologies. The implementation of these algorithms is subject to the realistic constraint that the communication rate, the memory capacities of agents and the computation precision are finite. The focus of this paper is on the study of the convergence time of the proposed quantized averaging algorithms. By appealing to random walks on graphs, we derive polynomial bounds on the expected convergence time of the algorithms presented.

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arXiv2010

Distributed coverage games for mobile visual sensor networks

Motivated by current challenges in data-intensive sensor networks, we formulate a coverage optimization problem for mobile visual sensors as a (constrained) repeated multi-player game. Each visual sensor tries to optimize its own coverage while minimizing the processing cost. We present two distributed learning algorithms where each sensor only remembers its own utility values and actions played during the last plays. These algorithms are proven to be convergent in probability to the set of (constrained) Nash equilibria and global optima of certain coverage performance metric, respectively.

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arXiv2005

Synchronous robotic networks and complexity of control and communication laws

This paper proposes a formal model for a network of robotic agents that move and communicate. Building on concepts from distributed computation, robotics and control theory, we define notions of robotic network, control and communication law, coordination task, and time and communication complexity. We then analyze a number of basic motion coordination algorithms such as pursuit, rendezvous and deployment.

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arXiv2004

Spatially-distributed coverage optimization and control with limited-range interactions

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.

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arXiv2003

A catalog of inverse-kinematics planners for underactuated systems on matrix groups

This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inverse-kinematics problems. We present a catalog of solutions for all underactuated systems on $\SE{2}$, $\SO{3}$ and $\SE{2}\times\real$ classified according to their controllability properties.

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arXiv2002

Motion planning and control problems for underactuated robots

Motion planning and control are key problems in a collection of robotic applications including the design of autonomous agile vehicles and of minimalist manipulators. These problems can be accurately formalized within the language of affine connections and of geometric control theory. In this paper we overview recent results on kinematic controllability and on oscillatory controls. Furthermore, we discuss theoretical and practical open problems as well as we suggest control theoretical approaches to them.

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arXiv2002

Computational problems for vector-valued quadratic forms

Given two real vector spaces $U$ and $V$, and a symmetric bilinear map $B: U\times U\to V$, let $Q_B$ be its associated quadratic map $Q_B$. The problems we consider are as follows: (i) are there necessary and sufficient conditions, checkable in polynomial-time, for determining when $Q_B$ is surjective?; (ii) if $Q_B$ is surjective, given $v\in V$ is there a polynomial-time algorithm for finding a point $u\in Q_B^{-1}(v)$?; (iii) are there necessary and sufficient conditions, checkable in polynomial-time, for determining when $B$ is indefinite? We present an alternative formulation of the problem of determining the image of a vector-valued quadratic form in terms of the unprojectivised Veronese surface. The relation of these questions with several interesting problems in Control Theory is illustrated.

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