Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Asymmetric Channels

In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights (possibly) dependent on the radio channels and we pose special attention to the effect of the propagation delay occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is reached with exponential convergence speed for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We provide a closed form expression for the global consensus, showing that the effect of delays is, in general, the introduction of a bias in the final decision. Finally, we exploit our closed form expression to devise a double-step consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters.Comment: To be published on IEEE Transactions on Signal Processin

Distributed Delay-Tolerant Strategies for Equality-Constraint Sum-Preserving Resource Allocation

This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at all-times. The proposed solutions can address various model nonlinearities, for example, due to quantization and/or saturation. Further, it allows to reach faster convergence or to robustify the solution against impulsive noise or uncertainties. We prove convergence over weakly connected networks using convex analysis and Lyapunov theory. Our findings show that convergence can be reached for general sign-preserving odd nonlinearity. We further propose delay-tolerant mechanisms to handle general bounded heterogeneous time-varying delays over the communication network of agents while preserving all-time feasibility. This work finds application in CPU scheduling and coverage control among others. This paper advances the state-of-the-art by addressing (i) possible nonlinearity on the agents/links, meanwhile handling (ii) resource-demand feasibility at all times, (iii) uniform-connectivity instead of all-time connectivity, and (iv) possible heterogeneous and time-varying delays. To our best knowledge, no existing work addresses contributions (i)-(iv) altogether. Simulations and comparative analysis are provided to corroborate our contributions

Fast-Convergent Dynamics for Distributed Resource Allocation Over Sparse Time-Varying Networks

In this paper, distributed dynamics are deployed to solve resource allocation over time-varying multi-agent networks. The state of each agent represents the amount of resources used/produced at that agent while the total amount of resources is fixed. The idea is to optimally allocate the resources among the group of agents by reducing the total cost functions subject to fixed amount of total resources. The information of each agent is restricted to its own state and cost function and those of its immediate neighbors. This is motivated by distributed applications such as in mobile edge-computing, economic dispatch over smart grids, and multi-agent coverage control. The non-Lipschitz dynamics proposed in this work shows fast convergence as compared to the linear and some nonlinear solutions in the literature. Further, the multi-agent network connectivity is more relaxed in this paper. To be more specific, the proposed dynamics even reaches optimal solution over time-varying disconnected undirected networks as far as the union of these networks over some bounded non-overlapping time-intervals includes a spanning-tree. The proposed convergence analysis can be applied for similar 1st-order resource allocation nonlinear dynamics. We provide simulations to verify our results

A Unified Analytical Look at Reynolds Flocking Rules

In this paper, we present a unified theoretical view of the so-called ``Flocking Rules of Reynolds'' introduced in 1987. No equations describing the rules or mathematical models of the mobile agents known as ``boids'' were presented in the original work by Reynolds. We show how to model a group of autonomous mobile agents by dynamic nets and achieve flocking by dissipation of the structural energy of the multi-agent system. As a by-product, we obtain a single protocol called the (alpha,alpha) protocol that encompasses all three flocking rules of Reynolds. We provide geometric interpretations of the advanced forms of some of these flocking rules. Simulation results are provided that demonstrate flocking of 100 agents towards a sink

Distributed consensus algorithms for wireless sensor networks: convergence analysis and optimization

Wireless sensor networks are developed to monitor areas of interest with the purpose of estimating physical parameters or/and detecting emergency events in a variety of military and civil applications. A wireless sensor network can be seen as a distributed computer, where spatially deployed sensor nodes are in charge of gathering measurements from the environment to compute a given function. The research areas for wireless sensor networks extend from the design of small, reliable hardware to low-complexity algorithms and energy saving communication protocols. Distributed consensus algorithms are low-complexity iterative schemes that have received increased attention in different fields due to a wide range of applications, where neighboring nodes communicate locally to compute the average of an initial set of measurements. Energy is a scarce resource in wireless sensor networks and therefore, the convergence of consensus algorithms, characterized by the total number of iterations until reaching a steady-state value, is an important topic of study. This PhD thesis addresses the problem of convergence and optimization of distributed consensus algorithms for the estimation of parameters in wireless sensor networks. The impact of quantization noise in the convergence is studied in networks with fixed topologies and symmetric communication links. In particular, a new scheme including quantization is proposed, whose mean square error with respect to the average consensus converges. The limit of the mean square error admits a closed-form expression and an upper bound for this limit depending on general network parameters is also derived. The convergence of consensus algorithms in networks with random topology is studied focusing particularly on convergence in expectation, mean square convergence and almost sure convergence. Closed-form expressions useful to minimize the convergence time of the algorithm are derived from the analysis. Regarding random networks with asymmetric links, closed-form expressions are provided for the mean square error of the state assuming equally probable uniform link weights, and mean square convergence to the statistical mean of the initial measurements is shown. Moreover, an upper bound for the mean square error is derived for the case of different probabilities of connection for the links, and a practical scheme with randomized transmission power exhibiting an improved performance in terms of energy consumption with respect to a fixed network with the same consumption on average is proposed. The mean square error expressions derived provide a means to characterize the deviation of the state vector with respect to the initial average when the instantaneous links are asymmetric. A useful criterion to minimize the convergence time in random networks with spatially correlated links is considered, establishing a sufficient condition for almost sure convergence to the consensus space. This criterion, valid also for topologies with spatially independent links, is based on the spectral radius of a positive semidefinite matrix for which we derive closed-form expressions assuming uniform link weights. The minimization of this spectral radius is a convex optimization problem and therefore, the optimum link weights minimizing the convergence time can be computed efficiently. The expressions derived are general and apply not only to random networks with instantaneous directed topologies but also to random networks with instantaneous undirected topologies. Furthermore, the general expressions can be particularized to obtain known protocols found in literature, showing that they can be seen as particular cases of the expressions derived in this thesis.Las redes de sensores inalámbricos se utilizan para monitorizar zonas de interés con el propósito final de estimar parámetros físicos y/o detectar situaciones de emergencia en gran variedad de aplicaciones militares y civiles. Una red de sensores inalámbricos puede ser considerada como un método de computación distribuido, donde nodos provistos de sensores toman medidas del entorno para calcular una función que depende de éstas. Las áreas de investigación comprenden desde el diseño de dispositivos hardware pequeños y fiables hasta algoritmos de baja complejidad o protocolos de comunicación de bajo consumo energético. Los algoritmos de consenso distribuidos son esquemas iterativos de baja complejidad que han suscitado mucha atención en diferentes campos debido a su gran espectro de aplicaciones, en los que nodos vecinos se comunican para calcular el promedio de un conjunto de medidas iniciales de la red. Dado que la energía es un recurso escaso en redes de sensores inalámbricos, la convergencia de dichos algoritmos de consenso, caracterizada por el número total de iteraciones hasta alcanzar un valor estacionario, es un importante tema de estudio. Esta tesis doctoral aborda problemas de convergencia y optimización de algoritmos de consenso distribuidos para la estimación de parámetros en redes de sensores inalámbricos. El impacto del ruido de cuantización en la convergencia se estudia en redes con topología fija y enlaces de comunicación simétricos. En particular, se propone un nuevo esquema que incluye el proceso de cuantización y se demuestra que el error cuadrático medio respecto del promedio inicial converge. Igualmente, se obtiene una expresión cerrada del límite del error cuadrático medio, y una cota superior para este límite que depende únicamente de parámetros generales de la red. La convergencia de los algoritmos de consenso en redes con topología aleatoria se estudia prestando especial atención a la convergencia en valor esperado, la convergencia en media cuadrática y la convergencia casi segura, y a partir del análisis se derivan expresiones cerradas útiles para minimizar el tiempo de convergencia. Para redes aleatorias con enlaces asimétricos, se obtienen expresiones cerradas del error cuadrático medio del estado suponiendo enlaces con probabilidad idéntica y con pesos uniformes, y se demuestra la convergencia en media cuadrática al promedio estadístico de las medidas iniciales. Se deduce una cota superior para el error cuadrático medio para el caso de enlaces con probabilidades de conexión diferentes y se propone, además, un esquema práctico con potencias de transmisión aleatorias, que mejora el rendimiento en términos de consumo de energía con respecto a una red fija. Las expresiones para el error cuadrático medio proporcionan una forma de caracterizar la desviación del vector de estado con respecto del promedio inicial cuando los enlaces instantáneos son asimétricos. Con el fin de minimizar el tiempo de convergencia en redes aleatorias con enlaces correlados espacialmente, se considera un criterio que establece una condición suficiente que garantiza la convergencia casi segura al espacio de consenso. Este criterio, que también es válido para topologías con enlaces espacialmente independientes, utiliza el radio espectral de una matriz semidefinida positiva para la cual se obtienen expresiones cerradas suponiendo enlaces con pesos uniformes. La minimización de dicho radio espectral es un problema de optimización convexa y, por lo tanto, el valor de los pesos óptimos puede calcularse de forma eficiente. Las expresiones obtenidas son generales y aplican no sólo para redes aleatorias con topologías dirigidas, sino también para redes aleatorias con topologías no dirigidas. Además, las expresiones generales pueden ser particularizadas para obtener protocolos conocidos en la literatura, demostrando que éstos últimos pueden ser considerados como casos particulares de las expresiones proporcionadas en esta tesis