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Decision-makers in foreign policy and national security are constantly confronted with an adversarial, networked environments. In such an environment, the "entities" (i.e., political establishments and military organizations) to whom those decision-makers are answerable are connected through a web of friendly and adversarial relationships. By a "networked political behavior" means that one's behavior can always propagate influences across the world for the world's connectedness. This paper contains a general, mathematical framework of rational agents' strategic interactions in the international security environment, which helps to draw theoretical and practical implications thereof. The theoretical framework called "games on signed graphs" examines how countries strive to survive and succeed in a globally networked environment through security and relation dynamics. Two games will be studied, with one called the power allocation game and the other called the signed network formation game. Theoretical findings, real-world applications, and possible extensions will be presented and discussed. [ABSTRACT FROM AUTHOR]

Abstract: Distributed averaging deals with a network of n >1 agents and the constraint that each agent is able to communicate only with its neighbors. The purpose of the distributed averaging problem is to devise a protocol which will enable all n agents to asymptotically determine in a decentralized manner, the average of the initial values of their scalar agreement variables. Most distributed averaging protocols involve a linear iteration which depends only on the current estimates of the average. Building on the idea proposed in , this paper investigates an augmented linear iteration for fast distributed averaging in which local memory is exploited. A thorough characterization of the behavior of the augmented system is obtained under appropriate assumptions. It is shown that the augmented linear iteration can solve the distributed averaging problem faster than the original linear iteration, but the adjustable parameter must be chosen carefully. The optimal choice of the parameter and the corresponding fastest rate of convergence are also provided in closed form. [Copyright &y& Elsevier]

Abstract: Dwell-time switching is a logic for orchestrating the switching between controllers in a family of candidate controllers in order to control a process with a highly uncertain model. An analysis is given of dwell-time switching which is appropriate to a variety of control problems in which the class of candidate controllers is either a finite set or a continuum of linear controllers. An example is given to illustrate the use of the paper’s main technical result. [Copyright &y& Elsevier]

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 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 deals with the problem of switching between several linear time-invariant (LTI) controllers—all of them capable of stabilizing a specific LTI process—in such a way that the stability of the closed-loop system is guaranteed for any switching sequence. We show that it is possible to find realizations for any given family of controller transfer matrices so that the closed-loop system remains stable, no matter how we switch among the controller. The motivation for this problem is the control of complex systems where conflicting requirements make a single LTI controller unsuitable. [Copyright &y& Elsevier]

By the distributed averaging problem is meant the problem of computing the average value of a set of numbers possessed by the agents in a distributed network using only communication between neighboring agents. Gossiping is a well-known approach to the problem which seeks to iteratively arrive at a solution by allowing each agent to interchange information with at most one neighbor at each iterative step. Crafting a gossiping protocol which accomplishes this is challenging because gossiping is an inherently collaborative process which can lead to deadlocks unless careful precautions are taken to ensure that it does not. Many gossiping protocols are request-based which means simply that a gossip between two agents will occur whenever one of the two agents accepts a request to gossip placed by the other. In this paper, we present three deterministic request-based protocols. We show by example that the first can deadlock. The second is guaranteed to avoid deadlocks by exploiting the idea of local ordering together with the notion of an agent’s neighbor queue; the protocol requires the simplest queue updates, which provides an in-depth understanding of how local ordering and queue updates avoid deadlocks. It is shown that a third protocol which uses a slightly more complicated queue update rule can lead to significantly faster convergence; a worst case bound on convergence rate is provided. [ABSTRACT FROM AUTHOR]

A hybrid observer is described for estimating the state of an m > 0 channel, n -dimensional, continuous-time, linear system of the form x ̇ = A x , y i = C i x , i ∈ { 1 , 2 , ... , m }. The system's state x is simultaneously estimated by m agents assuming each agent i senses y i and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph N (t) whose vertices correspond to agents and whose arcs depict neighbor relations. Agent i updates its estimate x i of x at "event times" t i 1 , t i 2 , t i 3 , ... using a local continuous-time linear observer and a local parameter estimator which iterates q times during each event time interval [ t i (s − 1) , t i s) , s ≥ 1 to obtain an estimate of x (t i s). Subject to the assumptions that none of the C i 's are zero, the neighbor graph N (t) is strongly connected for all time, and the system whose state is to be estimated is jointly observable, it is shown that for any number λ > 0 , it is possible to choose q and the local observer gains so that each estimate x i converges to x at least as fast as e − λ t does. This result holds whether or not agents communicate synchronously, although in the asynchronous case it is necessary to assume that N (t) changes in a suitably defined sense. Exponential convergence is also assured if the event time sequences of the m agents are slightly different than each other, although in this case only if the system being observed is exponentially stable; this limitation however, is primarily a robustness issue shared by all state estimators, centralized or not, which are operating in "open loop" in the face of small modeling errors. The result also holds facing abrupt changes in the number of vertices and arcs in the inter-agent communication graph upon which the algorithm depends. [ABSTRACT FROM AUTHOR]

This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator {comprising interconnected local estimators} is first described for estimating the state of a continuous and multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose graphs switch according to a switching signal. The estimator is guaranteed to solve the problem, provided a network-widely shared high gain condition achieving a form of spectrum separation is satisfied. As an alternative to sharing a common gain across the network, a fully distributed version of the estimator is also studied in which each agent adaptively adjusts a local gain, though the practicality of this approach is subject to a robustness issue common to adaptive control. A discrete-time version of the distributed state estimation problem is also studied, and a corresponding estimator based again on spectrum separation, but not high gain, is proposed for time-varying networks. For each scenario, it is explained how to construct the estimator so that the state estimation errors in the local estimators all converge to zero exponentially fast at a fixed but arbitrarily chosen rate, provided the network's graph is strongly connected for all time. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new supervisory control scheme, which is based on a control-relevant switching logic. Unlike most of the existing switching methods considering only estimator performance, the proposed scheme takes both estimator and controller performance into account. As an index to the controller performance, an iISS (integral-input-to-state stability) Lyapunov function is employed; it is ensured that the Lyapunov function satisfies a certain inequality. This Lyapunov-based switching is then coupled to the state-dependent dwell-time switching developed recently, and the state of the uncertain plant is shown to converge asymptotically. The proposed supervisory control scheme is applied to an input-constrained neurally stable linear plant. [Copyright &y& Elsevier]

Abstract: An approach to formulate geometric relations among distances between nodes as equality constraints is introduced in this paper to study the localization problem with imprecise distance information in sensor networks. These constraints can be further used to formulate optimization problems for distance estimation. The optimization solutions correspond to a set of distances that are consistent with the fact that sensor nodes live in the same plane or 3D space as the anchor nodes. These techniques serve as the foundation for most of the existing localization algorithms that depend on the sensors’ distances to anchors to compute each sensor''s location. [Copyright &y& Elsevier]

The paper deals with the supervisory control of a nonlinear uncertain system in which the switching is directed by the recently introduced state-dependent dwell-time switching logic. The proposed supervisory control architecture is shown to regulate to zero the state of the system without requiring the switching to stop in finite time. A significant class of systems to which the control architecture can be applied is the class of linear systems with input saturation. [Copyright &y& Elsevier]

The asymptotic convergence of a switched nonlinear system in the presence of disturbances is studied. The system switches among a family of integral input-to-state stable systems. The time between two consecutive switchings is not less than a value τD. This dwell-time τD is allowed to take different values according to a function whose argument is the state of the system at the switching times. We propose a dwell-time function which depends on the comparison functions which characterize the integral input-to-state stability property and guarantees the state of the switched system to converge to zero under the action of disturbances with “bounded energy”. The main feature of the analysis is that it does not rely on the property for the switching to stop in finite time. The two important cases of locally exponentially stable and feedforward systems are analyzed in detail. [Copyright &y& Elsevier]

In this paper we describe a framework for deterministic adaptive control which involves logic-based switching among a family of candidate controllers. We compare it with more conventional adaptive control techniques that rely on continuous tuning, emphasizing how switching and logic can be used to overcome some of the limitations of traditional adaptive control. The issues are discussed in a tutorial, non-technical manner and illustrated with specific examples. [Copyright &y& Elsevier]

We address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers. We present a new hysteresis-based switching logic, designed specifically for this purpose, and derive a bound on the number of switches produced by this logic on an arbitrary time interval. The resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics. [Copyright &y& Elsevier]

The subject of this paper is hybrid control of nonlinear systems with large-scale uncertainty. We describe a high-level controller, called a “supervisor”, which orchestrates logic-based switching among a family of candidate controllers. We show that in this framework, the problem of controller design at the lower level can be reduced to finding an integral-input-to-state stabilizing control law for an appropriate system with disturbance inputs. Employing the recently introduced “scale-independent hysteresis” switching logic, we prove that in the case of purely parametric uncertainty with unknown parameters taking values in a finite set the switching terminates in finite time and state regulation is achieved. [Copyright &y& Elsevier]

In its simplest form the well known consensus problem for a networked family of autonomous agents is to devise a set of protocols or update rules, one for each agent, which can enable all of the agents to adjust or tune their "agreement variables" to the same value by utilizing real-time information obtained from their "neighbors" within the network. The aim of this paper is to study the problem of achieving a consensus in the face of limited information transfer between agents. By this it is meant that instead of each agent receiving an agreement variable or real-valued state vector from each of its neighbors, it receives a linear function of each state instead. The specific problem of interest is formulated and provably correct algorithms are developed for a number of special cases of the problem. [ABSTRACT FROM AUTHOR]

Abstract: Gossiping is a distributed process whose purpose is to enable the members of a group of autonomous agents to asymptotically determine in a decentralized manner, the average of the initial values of their scalar gossip variables. This paper analyzes the accelerated gossip algorithms, first proposed in Cao, Spielman, and Yeh (2006), in which local memory is exploited by installing shift-registers at each agent. For the two-register case, the existence of the desired convergence is established under a symmetry assumption by separately studying the convergence in expectation and in mean square. In particular, the optimal rate of convergence in expectation is derived which is faster than that of the standard gossip algorithm, and a sufficient condition on the adjustable parameter for the convergence in mean square is provided. These theoretical results are validated for some classes of networks by comparison with existing empirical data. More general multi-register cases are also discussed. [Copyright &y& Elsevier]

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]

Explores the fundamental limits of the use of quartz tuning forks as force detectors in scanned probe microscopy. Root mean square Brownian motion exhibited by the fore sensors; Detection of dissipative and reactive forces on approach to the sample; Closed loop responses yielded by the conventional proportional-integral feedback control.