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

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Connectivity and Consensus in Multi-Agent Systems with Uncertain Links

In the analysis and design of a multi-agent system (MAS), studying the graph representing the system is essential. In particular, when the communication links in a MAS are subject to uncertainty, a random graph is used to model the system. This type of graph is represented by a probability matrix, whose elements reflect the probability of the existence of the corresponding edges in the graph. This probability matrix needs to be adequately estimated. In this thesis, two approaches are proposed to estimate the probability matrix in a random graph. This matrix is time-varying and is used to determine the network configuration at different points in time. For evaluating the probability matrix, the connectivity of the network needs to be assessed first. It is to be noted that connectivity is a requirement for the convergence of any consensus algorithm in a network. The probability matrix is used in this work to study the consensus problem in a leader-follower asymmetric MAS with uncertain communication links. We propose a novel robust control approach to obtain an approximate agreement among agents under some realistic assumptions. The uncertainty is formulated as disturbance, and a controller is developed to debilitate it. Under the proposed controller, it is guaranteed that the consensus error satisfies the global L2-gain performance in the presence of uncertainty. The designed controller consists of two parts: one for time-varying links and one for time-invariant links. Simulations demonstrate the effectiveness of the proposed methods

Connectivity and Consensus in Multi-Agent Systems with Uncertain Links

In the analysis and design of a multi-agent system (MAS), studying the graph representing the system is essential. In particular, when the communication links in a MAS are subject to uncertainty, a random graph is used to model the system. This type of graph is represented by a probability matrix, whose elements reflect the probability of the existence of the corresponding edges in the graph. This probability matrix needs to be adequately estimated. In this thesis, two approaches are proposed to estimate the probability matrix in a random graph. This matrix is time-varying and is used to determine the network configuration at different points in time. For evaluating the probability matrix, the connectivity of the network needs to be assessed first. It is to be noted that connectivity is a requirement for the convergence of any consensus algorithm in a network. The probability matrix is used in this work to study the consensus problem in a leader-follower asymmetric MAS with uncertain communication links. We propose a novel robust control approach to obtain an approximate agreement among agents under some realistic assumptions. The uncertainty is formulated as disturbance, and a controller is developed to debilitate it. Under the proposed controller, it is guaranteed that the consensus error satisfies the global L2-gain performance in the presence of uncertainty. The designed controller consists of two parts: one for time-varying links and one for time-invariant links. Simulations demonstrate the effectiveness of the proposed methods

Nonlinear dynamics and applications of MEMS and NEMS resonators.

Rich nonlinear behaviours have been observed in microelectromechanical and nanoelectromechanical systems (MEMS and NEMS) resonators. This dissertation has performed a systematic study of nonlinear dynamics in various MEMS and NEMS resonators that appear to be single, two coupled, arrayed, parametric driven and coupled with multiple-fields, with the aim of exploring novel applications. New study on dynamic performance of a single carbon nanotube resonator taking account of the surface induced initial stress has been performed. It is found that the initial stress causes the jumping points, the whirling and chaotic motions to appear at higher driving forces. Chaotic synchronization of two identical MEMS resonators has been theoretically achieved using Open-Plus-Closed-Loop (OPCL) method, and the coupled resonating system is designed as a mass detector that is believed to possess high resistance to noise. The idea of chaotic synchronization is then popularized into wireless sensor networks for the purpose of achieving secure communication. The arising of intrinsic localised mode has been studied in microelectromechanical resonators array that is designed intentionally for an energy harvester, which could potentially be used to achieve high/concentrated energy output. Duffing resonators with negative and positive spring constants can exhibit chaotic behaviour. Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos. Based on the principle of nanomechanical transistor and quantum shuttle mechanism, a high sensitive mass sensor that consists of two mechanically coupled NEMS resonators has been postulated, and the mass sensor which can be realized in large-scale has also been investigated and verified. Furthermore, an novel transistor that couples three physical fields at the same time, i.e. mechanical, optical and electrical, has been designed, and the coupled opto-electro-mechanical simulation has been performed. It is shown from the dynamic analysis that the stable working range of the transistor is much wider than that of the optical wave inside the cavity