Persistence based analysis of consensus protocols for dynamic graph networks

This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These results are based on the analysis of a system switching between piecewise constant and time-invariant dynamics. This work introduces a new analysis technique relying upon classical notions of persistence of excitation to study the convergence properties of the time-varying multi-agent dynamics. Since the individual edge weights pass through singularities and vary with time, the closed-loop dynamics consists of a non-autonomous linear system. Instead of simplifying to a piecewise continuous switched system as in literature, smooth variations in edge weights are allowed, albeit assuming an underlying persistence condition which characterizes sufficient inter-agent communication to reach consensus. The consensus task is converted to edge-agreement in order to study a stabilization problem to which classical persistence based results apply. The new technique allows precise computation of the rate of convergence to the consensus value.Comment: This article contains 7 pages and includes 4 figures. it is accepted in 13th European Control Conferenc

Distributed Least Squares Algorithm for Continuous-time Stochastic Systems Under Cooperative Excitation Condition

In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS) algorithm based on diffusion strategy is proposed such that the sensors can cooperatively estimate the unknown time-invariant parameter vector from continuous-time noisy signals. By using the martingal estimation theory and Ito formula, we provide upper bounds for the estimation error of the proposed distributed LS algorithm, and further obtain the convergence results under a cooperative excitation condition. Compared with the existing results, our results are established without using the boundedness or persistent excitation (PE) conditions of regression signals. We provide simulation examples to show that multiple sensors can cooperatively accomplish the estimation task even if any individual can not

Stability of FFLS-based diffusion adaptive filter under a cooperative excitation condition

In this paper, we consider the distributed filtering problem over sensor networks such that all sensors cooperatively track unknown time-varying parameters by using local information. A distributed forgetting factor least squares (FFLS) algorithm is proposed by minimizing a local cost function formulated as a linear combination of accumulative estimation error. Stability analysis of the algorithm is provided under a cooperative excitation condition which contains spatial union information to reflect the cooperative effect of all sensors. Furthermore, we generalize theoretical results to the case of Markovian switching directed graphs. The main difficulties of theoretical analysis lie in how to analyze properties of the product of non-independent and non-stationary random matrices. Some techniques such as stability theory, algebraic graph theory and Markov chain theory are employed to deal with the above issue. Our theoretical results are obtained without relying on the independency or stationarity assumptions of regression vectors which are commonly used in existing literature.Comment: 12 page

Hessian Estimation Based Adaptive and Cooperative Extremum Localization

The thesis is on Hessian estimation based adaptive and cooperative extremum localization via a single mobile sensory agent as well as a network of multiple such agents. First, we develop a continuous time adaptive extremum localization of an arbitrary quadratic function F(·) based on Hessian estimation, using the measured signal intensity via a single mobile sensory agent. A gradient based adaptive Hessian parameter estimation and extremum localization scheme is developed considering a linear parametric model of field variations. Next, we extend the proposed single agent based Hessian estimation and extremum localization scheme to consensus based cooperative distributed scheme to be implemented by a network of such sensory agents.For the networked multi-agent case, a consensus term is added to the base adaptive laws to obtain enhanced estimation cooperatively. Stability and convergence analysis of the proposed scheme is studied, establishing asymptotic convergence of the Hessian parameters and location estimates to their true values robustly, provided that the motion of agent(s) satisfies certain persistence of excitation(PE) conditions. Furthermore, we show that for a network of connected agents, the PE requirements can be distributed to the agents so that the requirement on each agent is more relaxed and feasible. Later, we design an adaptive motion control scheme for steering a mobile sensory agent in 2D toward the source of a signal field F(·) using the signal intensity the agent continuously measures at its current location. The proposed adaptive control design is based on the Hessian estimation based adaptive extremum localization. Results are displayed to verify that the proposed scheme is stable, provides asymptotic convergence of the Hessian parameter and extremum location estimates to their true values and the agent location to the source location, robustly to signal measurement noises

Resilient Distributed Parameter Estimation in Sensor Networks

In this paper, we study the problem of parameter estimation in a sensor network, where the measurements and updates of some sensors might be arbitrarily manipulated by adversaries. Despite the presence of such misbehaviors, normally behaving sensors make successive observations of an unknown $d$-dimensional vector parameter and aim to infer its true value by cooperating with their neighbors over a directed communication graph. To this end, by leveraging the so-called dynamic regressor extension and mixing procedure, we transform the problem of estimating the vector parameter to that of estimating $d$ scalar ones. For each of the scalar problem, we propose a resilient combine-then-adapt diffusion algorithm, where each normal sensor performs a resilient combination to discard the suspicious estimates in its neighborhood and to fuse the remaining values, alongside an adaptation step to process its streaming observations. With a low computational cost, this estimator guarantees that each normal sensor exponentially infers the true parameter even if some of them are not sufficiently excited