Search

This paper considers a deterministic susceptible-infected-susceptible (SIS) networked bivirus epidemic model (termed the bivirus model for short), in which two competing viruses spread through a set of populations (nodes) connected by two graphs, which may be different if the two viruses have different transmission pathways. The networked dynamics can give rise to complex equilibria patterns, and most current results identify conditions on the model parameters for convergence to the healthy equilibrium (where both viruses are extinct) or a boundary equilibrium (where one virus is endemic and the other is extinct). However, there are only limited results on coexistence equilibria (where both viruses are endemic). This paper establishes a set of "counting" results which provide lower bounds on the number of coexistence equilibria and, perhaps more importantly, establish properties on the local stability/instability properties of these equilibria. In order to do this, we employ the Poincaré--Hopf theorem but with significant modifications to overcome several challenges arising from the bivirus system model, such as the fact that the system dynamics do not evolve on a manifold in the typical sense required to apply Poincaré--Hopf theory. Subsequently, Morse inequalities are used to tighten the counting results, under the reasonable assumption that the bivirus system is a Morse--Smale dynamical system. Numerical examples are provided which demonstrate the presence of multiple attractor equilibria and multiple coexistence equilibria. [ABSTRACT FROM AUTHOR]

In “stand-off” scenarios, an estimate of the bearing to an emitter can be easily calculated from measurements of the received frequency, position, and velocity of receivers. This technique is only effective if the measured frequencies can be reliably associated with a single emitter that is far away. We show how to determine if the receivers’ measurements correspond to a single emitter in a stand-off scenario, eliminate outliers, and estimate the unknown transmit frequency. [ABSTRACT FROM AUTHOR]

In a network of cooperating unmanned aerial vehicles (UAVs), individual UAVs usually need to localize themselves in a shared and generally global frame. This paper studies the localization problem for a group of UAVs navigating in three-dimensional space with limited shared information, viz., noisy distance measurements are the only type of interagent sensing that is available, and only one UAV knows its global coordinates, the others being GPS denied. Initially, for a two-agent problem, but easily generalized to some multiagent problems, this paper first establishes constraints on the minimum number of distance measurements required to achieve the localization. This paper then proposes a composite algorithm based on semidefinite programming (SDP) in a first step, followed by maximum likelihood estimation using gradient descent on a manifold initialized by the SDP calculation. The efficacy of the algorithm is verified with experimental noisy flight data. [ABSTRACT FROM AUTHOR]

In this paper, we study rigid formation control systems modelled by double integrators. Two kinds of double-integrator formation systems are considered, namely formation stabilisation systems and flocking control systems. Novel observations on the measurement requirement, the null space and eigenvalues of the system Jacobian matrix will be provided, which reveal important properties of system dynamics and the associated convergence results. We also establish some new links between single-integrator formation systems and double-integrator formation systems via a parameterised Hamiltonian system, which, in addition, provide novel stability criteria for different equilibria in double-integrator formation systems by using available results in single-integrator formation systems. [ABSTRACT FROM AUTHOR]

Self-localization and formation control tasks are considered when each agent in a multiagent formation observes its neighbors but does not communicate. Each agent is restricted to a predefined motion type on a 2-D plane and collects bearing-only measurements over a time interval to localize neighboring agents. The localization process is used by a three agent formation to achieve velocity consensus combined with formation shape control. Simulations are provided and noisy bearing measurements are investigated. [ABSTRACT FROM PUBLISHER]

John Moore was born in Lungling, China on 3 April 1941 and died in Canberra on 19 January 2013. He was an electrical engineer who spent most of his distinguished career at the University of Newcastle and the Australian National University following industrial experience and graduate education in Silicon Valley, California. He was a Fellow of the Institute of Electrical and Electronic Engineers, the Australian Academy of Science and the Australian Academy of Technological Sciences and Engineering, achieving all honours at a comparatively early age, and was recognized principally for his contributions to the field of control systems. [ABSTRACT FROM AUTHOR]

Formation shape control for a collection of point agents is concerned with devising decentralized control laws which ensure that the formation will move so that certain interagent distances approximate prescribed values as closely as possible. Such laws are often derived using steepest descent of a potential function which is invariant under translation and rotation, and then critical formations are those that are fixed under the evolution of the decentralized control dynamics, i.e., those corresponding to equilibrium points of the control dynamics. Using a specific and frequently used potential function for formation control, this paper introduces tools from Morse theory and complex algebraic geometry to estimate the number of critical formations of N agents on a line. We show that there are at least 2N - 1 equilibrium points and at most 3N-1 isolated equilibria. Moreover, bounds on the number of equilibrium points with a k-dimensional stable manifold (the so called Morse-index) are established. We show that generically there are exactly five critical formations for three agents on a line, and exactly 27 complex critical formations for four agents on a line, where a complex critical formation is defined as an equilibrium point of the gradient flow with complex, not necessarily real, coordinates. Except for a single critical formation, no two or more of the agents in the other 26 critical formations are collocated. [ABSTRACT FROM AUTHOR]

This paper studies networks where all nodes are distributed on a unit square A\buildrel\triangle\over= [- 1\over 2, 1\over 2]^2 following a Poisson distribution with known density \rho and a pair of nodes separated by an Euclidean distance x are directly connected with probability gr\rho(x){\buildrel{\triangle}\over{=}} g(x/r\rho), independent of the event that any other pair of nodes are directly connected. Here, g:[0,\infty)\rightarrow [0,1] satisfies the conditions of rotational invariance, nonincreasing monotonicity, integral boundedness, and g\left (x\right)=o(1/(x^2\log^2x)); further, r\rho=\sqrt {(\log \rho +b)/(C\rho)} where C=\int\Re^{2}g(\left \Vert {\mmb {x}}\right \Vert)d {\mmb {x}} and b is a constant. Denote the aforementioned network by \cal G\left (\cal X\rho,gr\rho,A\right). We show that as \rho \rightarrow \infty, 1) the distribution of the number of isolated nodes in \cal G\left (\cal X\rho,gr\rho,A\right) converges to a Poisson distribution with mean e^-b; 2) asymptotically almost surely (a.a.s.) there is no component in \cal G\left (\cal X\rho,gr\rho,A\right) of fixed and finite order k> 1; c) a.a.s. the number of components with an unbounded order is one. Therefore, as \rho \rightarrow \infty, the network a.a.s. contains a unique unbounded component and isolated nodes only; a sufficient and necessary condition for \cal G\left (\cal X\rho,gr\rho,A\right) to be a.a.s. connected is that there is no isolated node in the network, which occurs when b\rightarrow \infty as \rho \rightarrow \infty. These results expand recent results obtained for connectivity of random geometric graphs from the unit disk model and the fewer results from the log-normal model to the more general and more practical random connection model. [ABSTRACT FROM AUTHOR]

The sensor network localization problem is one of determining the Euclidean positions of all sensors in a network given knowledge of the Euclidean positions of some, and knowledge of a number of inter-sensor distances. This paper identifies graphical properties which can ensure unique localizability, and further sets of properties which can ensure not only unique localizability but also provide guarantees on the associated computational complexity, which can even be linear in the number of sensors on occasions. Sensor networks with minimal connectedness properties in which sensor transmit powers can be increased to increase the sensing radius lend themselves to the acquiring of the needed graphical properties. Results are presented for networks in both two and three dimensions. [ABSTRACT FROM AUTHOR]

We examine the problem of optimal bearing-only localization of a single target using synchronous measurements from multiple sensors. We approach the problem by forming geometric relationships between the measured parameters and their corresponding errors in the relevant emitter localization scenarios. Specifically, we derive a geometric constraint equation on the measurement errors in such a scenario. Using this constraint, we formulate the localization task as a constrained optimization problem that can be performed on the measurements in order to provide the optimal values such that the solution is consistent with the underlying geometry. We illustrate and confirm the advantages of our approach through simulation, offering detailed comparison with traditional maximum likelihood (TML) estimation. [ABSTRACT FROM AUTHOR]

This paper studies the problem of controlling the shape of a formation of point agents in the plane. A model is considered where the distance between certain agent pairs is maintained by one of the agents making up the pair; if enough appropriately chosen distances are maintained, with the number growing linearly with the number of agents, then the shape of the formation will be maintained. The detailed question examined in the paper is how one may construct decentralized nonlinear control laws to be operated at each agent that will restore the shape of the formation in the presence of small distortions from the nominal shape. Using the theory of rigid and persistent graphs, the question is answered. As it turns out, a certain submatrix of a matrix known as the rigidity matrix can be proved to have nonzero leading principal minors, which allows the determination of a stabilizing control law. [ABSTRACT FROM AUTHOR]

In complex electromagnetic environments it can often be difficult to determine whether signals received by an antenna array emanated from the same source. The failure to appropriately assign signal reception events to the correct emission event makes accurate localization of the signal source impossible. In this paper we show that as the received signal events must lie on the light-cone of the emission event the Cayley–Menger determinate calculated from using the light-cone geodesic distances between received signals must be zero. This result enables us to construct an algorithm for sorting received signals into groups corresponding to the same far-field emission. [ABSTRACT FROM AUTHOR]

A GPS-denied unmanned aerial vehicle (UAV) (Agent B) is localized through inertial navigation system alignment with the aid of a nearby GPS-equipped UAV (Agent A), which broadcasts its position at several time instants. Agent B measures the signals' direction of arrival with respect to Agent B's inertial navigation frame. Semidefinite programming and the orthogonal Procrustes algorithm are employed, and accuracy is improved through maximum likelihood estimation. The method is validated using flight data and simulations. A three-agent extension is explored. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we discuss quantization effects in rigid formation control systems when target formations are described by interagent distances. Because of practical sensing and measurement constraints, we consider in this paper distance measurements in their quantized forms. We show that under gradient‐based formation control, in the case of uniform quantization, the distance errors converge locally to a bounded set whose size depends on the quantization error, while in the case of logarithmic quantization, all distance errors converge locally to zero. A special quantizer involving the signum function is then considered with which all agents can only measure coarse distances in terms of binary information. In this case, the formation converges locally to a target formation within a finite time. Lastly, we discuss the effect of asymmetric uniform quantization on rigid formation control. [ABSTRACT FROM AUTHOR]

In this paper, we investigate probabilistic stability of Kalman filtering over fading channels modeled by *-mixing random processes, where channel fading is allowed to generate non-stationary packet dropouts with temporal and/or spatial correlations. Upper/lower almost sure (a.s.) stabilities and absolutely upper/lower a.s. stabilities are defined for characterizing the sample-path behaviors of the Kalman filtering. We prove that both upper and lower a.s. stabilities follow a zero–one law, i.e., these stabilities must happen with a probability either zero or one, and when the filtering system is one-step observable, the absolutely upper and lower a.s. stabilities can also be interpreted using a zero–one law. We establish general stability conditions for (absolute) upper and lower a.s. stabilities. In particular, with one-step observability, we show the equivalence between absolutely a.s. stabilities and a.s. ones, and necessary and sufficient conditions in terms of packet arrival rate are derived; for the so-called non-degenerate systems, we also manage to give a necessary and sufficient condition for upper a.s. stability. [ABSTRACT FROM AUTHOR]

To cope with an exponentially increasing demand on mobile data traffic in cellular networks, high-capacity WiFi and device-to-device networks can be exploited as a complementary means to offload and reduce the traffic load of cellular networks. This paper proposes a novel cooperative content dissemination strategy for a heterogeneous network consisting of different types of devices, such as WiFi access points (APs), smartphones, and intelligent vehicles. The proposed strategy offloads a significant proportion of data traffic from cellular networks to WiFi or device-to-device networks using ad hoc connections that opportunistically emerge when mobile devices move and meet one another. The strategy is particularly suited for dissemination of delay-tolerant content. Detailed analysis is provided for the content dissemination process in heterogeneous mobile networks adopting the proposed strategy. On this basis, the optimal parameter settings for the content dissemination strategy are discussed. Simulation and numerical results show that the proposed strategy significantly reduces the amount of data traffic for cellular networks while guaranteeing the successful delivery of content. [ABSTRACT FROM AUTHOR]

Heterogeneous formation shape control with interagent bearing and distance constraints involves the design of a distributed control law that ensures the formation moves such that these interagent constraints are achieved and maintained. This paper looks at the design of a distributed control scheme to solve different formation shape control problems in an ambient two-dimensional space with bearing, distance and mixed bearing and distance constraints. The proposed control law allows the agents in the formation to move in any direction on a half-plane and guarantees that despite this freedom, the proposed shape control algorithm ensures convergence to a formation shape meeting the prescribed constraints. This work provides an interesting and novel contrast to much of the existing work in formation control where distance-only constraints are typically maintained and where each agent's motion is typically restricted to follow a very particular path. A stability analysis is sketched, and a number of illustrative examples are also given. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the problem of localization and circumnavigation of a group of targets, which are either stationary or moving slowly with unknown speed, by a single agent. An estimator is proposed, initially for the stationary target case, to localize the targets and the center of mass of them as well as a control law that forces the agent to move on a circular trajectory around the center of mass of the targets such that both the estimator and the controller are exponentially stable. Then the case where the targets might experience slow but possibly steady movements is studied. The system inputs include the agent's position and the bearing angles to the targets. The performance of the proposed algorithms is verified through simulations. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In multihop localization procedures where not every node at unknown positions (i.e., sensors) can directly measure distances to nodes at known positions (i.e., anchors), sensor localization errors normally propagate (i.e., increase) as sensors progressively more distant from anchors are localized. To understand error propagation, we consider a primitive localization scenario: Nodes are deployed within a disk according to a homogeneous Poisson point process, the nodes around the disk center are anchors, the other nodes are sensors, and sensors are localized from the disk center to the outside in a hop-by-hop manner. Supposing noisy distance measurements between adjacent nodes, we analyze the quantitative relationship among sensor localization errors, minimal hop counts from sensors to anchors, the sensor density, and the noise level of distance measurements. This relationship clearly reflects the properties of error propagation and is greatly helpful to the design and deployment of large-scale sensor networks. Finally, a simulation analysis based on actual localization procedures and the Cramér–Rao lower bound confirms our results. [ABSTRACT FROM PUBLISHER]

A novel analytical approach is proposed to approximate and correct the bias in localization problems in $n$-dimensional space ($n=2$ or 3) with $N$ ($N>=n$) independently usable measurements (such as distance, bearing, time difference of arrival (TDOA), etc.). Here, $N$ is often but not always the same as the number of sensors. This new method mixes Taylor series and Jacobian matrices to determine the bias and leads in the case when $N=n$ to an easily calculated analytical bias expression; however, when $N$ is greater than $n$, the nature of the calculation is more complicated in that a further step is required. The proposed novel method is generic, which means that it can be applied to different types of measurements. To illustrate this approach we analyze the proposed method in three situations. Monte Carlo simulation results verify that, when the underlying geometry is a good geometry (which allows the location of the target to be obtained with acceptable mean square error (MSE)), the proposed approach can correct the bias effectively in space of dimension 2 or 3 with an arbitrary number of independent usable measurements. In addition the proposed method is applicable irrespective of the type of measurement (range, bearing, TDOA, etc.). [ABSTRACT FROM AUTHOR]

In this paper, we study the information propagation process in a 1-D mobile ad hoc network formed by vehicles Poissonly distributed on a highway and traveling in the same direction at randomly distributed speeds that are independent between vehicles. Considering a model in which time is divided into time slots of equal length and each vehicle changes its speed at the beginning of each time slot, independent of its speed in other time slots, we derive analytical formulas for the fundamental properties of the information propagation process and the information propagation speed (IPS). Using the formulas, one can straightforwardly study the impact on the IPS of various parameters such as radio range, vehicular traffic density, and time variation of vehicle speed. The accuracy of the results is validated using simulations. The research provides useful guidelines on the design of vehicular ad hoc networks (VANETs). [ABSTRACT FROM PUBLISHER]

In this paper, we study transmission power to secure the connectivity of a network. Instead of requiring all nodes to be connected, we require that only a large fraction (e.g., 95%) be connected, which is called the giant component. We show that, with this slightly relaxed requirement on connectivity, significant energy savings can be achieved for a large-scale network. In particular, we assume that a total of n nodes are randomly independently uniformly distributed in a unit square in R2, that each node has uniform transmission power, and that any two nodes are directly connected if and only if the power that was received by one node from the other node, as determined by the log-normal shadowing model, is larger than or equal to a given threshold. First, we derive an upper bound on the minimum transmission power at which the probability of having a giant component of order above qn for any fixed q Ȇ (0, 1) tends to one as n →∞. Second, we derive a lower bound on the minimum transmission power at which the probability of having a connected network tends to one as n →∞. We then show that the ratio of the aforementioned transmission power that was required for a giant component to the transmission power that was required for a connected network tends to zero as n →∞. This result implies significant energy savings if we require that only most nodes (e.g., 95%) be connected rather than requiring all nodes to be connected. This result is also applicable for any other arbitrary channel model that satisfies certain intuitively reasonable conditions. [ABSTRACT FROM AUTHOR]

This paper considers localization of a source or a sensor from distance measurements. We argue that linear algorithms proposed for this purpose are susceptible to poor noise performance. Instead given a set of sensors/anchors of known positions and measured distances of the source/sensor to be localized from them we propose a potentially nonconvex weighted cost function whose global minimum estimates the location of the source/sensor one seeks. The contribution of this paper is to provide nontrivial ellipsoidal and polytopic regions surrounding these sensors/anchors of known positions, such that if the object to be localized is in this region, localization occurs by globally exponentially convergent gradient descent in the noise free case. Exponential convergence in the noise free case represents practical convergence as it ensures graceful performance degradation in the presence of noise. These results guide the deployment of sensors/anchors so that small subsets can be made responsible for practical localization in geographical areas determined by our approach. [ABSTRACT FROM AUTHOR]

This paper uses recently established properties of compositions of directed graphs together with results from the theory of nonhomogeneous Markov chains to derive worst case convergence rates for the headings of a group of mobile autonomous agents which arise in connection with the widely studied Vicsek consensus problem. The paper also uses graph-theoretic constructions to solve modified versions of the Vicsek problem in which there are measurement delays, asynchronous events, or a group leader. In all three cases the conditions under which consensus is achieved prove to be almost the same as the conditions under which consensus is achieved in the synchronous, delay-free, leaderless case. [ABSTRACT FROM AUTHOR]

This paper presents new graph-theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments. The concepts of rooted, strongly rooted, and neighbor-shared are defined, and conditions are derived for compositions of sequences of directed graphs to be of these types. The graph of a stochastic matrix is defined, and it is shown that under certain conditions the graph of a Sarymsakov matrix and a rooted graph are one and the same. As an illustration of the use of the concepts developed in this paper, graphtheoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied Vicsek consensus problem. [ABSTRACT FROM AUTHOR]

This article discusses cooperative stabilization control of rigid formations via an event-based approach. We first design a centralized event-based formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the triggering condition, event function, and triggering behavior are discussed in detail, and the exponential convergence of the event-based formation system is guaranteed. [ABSTRACT FROM AUTHOR]