Now showing 1 - 10 of 33
PublicationEffects of Delay on the Functionality of Large-scale Networks(2008-02-01) Papachristodoulou, Antonis; Jadbabaie, AliNetworked systems are common across engineering and the physical sciences. Examples include the Internet, coordinated motion of multi-agent systems, synchronization phenomena in nature etc. Their robust functionality is important to ensure smooth operation in the presence of uncertainty and unmodelled dynamics. Many such networked systems can be viewed under a unified optimization framework and several approaches to assess their nominal behaviour have been developed. In this paper, we consider what effect multiple, non-commensurate (heterogeneous) communication delays can have on the functionality of large-scale networked systems with nonlinear dynamics. We show that for some networked systems, the structure of the delayed dynamics allows functionality to be retained for arbitrary communication delays, even for switching topologies under certain connectivity conditions; whereas in other cases the loop gains have to be compensated for by the delay size, in order to render functionality delay-independent for arbitrary network sizes. Consensus reaching in multi-agent systems and stability of network congestion control for the Internet are used as examples. The differences and similarities of the two cases are explained in detail, and the application of the methodology to other technological and physical networks is discussed. PublicationConsensus Over Martingale Graph Processes(2012-06-01) Fazeli, Arastoo; Jadbabaie, AliIn this paper, we consider a consensus seeking process based on repeated averaging in a randomly changing network. The underlying graph of such a network at each time is generated by a martingale random process. We prove that consensus is reached almost surely if and only if the expected graph of the network contains a directed spanning tree. We then provide an example of a consensus seeking process based on local averaging of opinions in a dynamic model of social network formation which is a martingale. At each time step, individual agents randomly choose some other agents to interact with according to some arbitrary probabilities. The interaction is one-sided and results in the agent averaging her opinion with those of her randomly chosen neighbors based on the weights she assigns to them. Once an agent chooses a neighbor, the weights are updated in such a way that the expected values of the weights are preserved. We show that agents reach consensus in this random dynamical network almost surely. Finally, we demonstrate that a Polya Urn process is a martingale process, and our prior results in  is a special case of the model proposed in this paper. PublicationTargeted Marketing and Seeding Products with Positive Externality(2012-10-01) Fazeli, Arastoo; Jadbabaie, AliWe study a strategic model of marketing in social networks in which two firms compete for the spread of their products. Firms initially determine the production cost of their product, which results in the payoff of the product for consumers, and the number and the location of the consumers in a network who receive the product as a free offer. Consumers play a local coordination game over a fixed network which determines the dynamics of the spreading of products. Assuming myopic best response dynamics, consumers choose a product based on the payoff received by actions of their neighbors. This local update dynamics results in a game-theoretic diffusion process in the network. Utilizing earlier results in the literature, we derive a lower and an upper bound on the proportion of product adoptions which not only depend on the number of initial seeds but also incorporate their locations as well. Using these bounds, we then study which consumers should be chosen initially in a network in order to maximize product adoptions for firms. We show consumers should be seeded based on their eigenvector centrality in the network. We then consider a game between two firms aiming to optimize their products adoptions while considering their fixed budgets. We describe the Nash equilibrium of the game between firms in star and k-regular networks and compare the equilibrium with our previous results. PublicationDistributed coverage verification in sensor networks without location information(2008-12-11) Tahbaz-Salehi, Alireza; Jadbabaie, AliIn this paper, we present a distributed algorithm for detecting coverage holes in a sensor network with no location information. We demonstrate how, in the absence of localization devices, simplicial complexes and tools from computational homology can be used in providing valuable information on the properties of the cover. In particular, we capture the combinatorial relationships among the sensors by the means of the Rips complex, which is the generalization of the proximity graph of the network to higher dimensions. Our approach is based on computation of a certain generator of the first homology of the Rips complex of the network. We formulate the problem of localizing coverage holes as an optimization problem to compute the sparsest generator of the first homology classes. We also demonstrate how subgradient methods can be used in solving this optimization problem in a distributed manner. Finally, non-trivial simulations are provided that illustrate the performance of our algorithm. PublicationBearing-Only Control Laws For Balanced Circular(2008-06-28) Moshtagh, Nima; Michael, Nathan; Jadbabaie, Ali; Daniilidis, KostasFor a group of constant-speed ground robots, a simple control law is designed to stabilize the motion of the group into a balanced circular formation using a consensus approach. It is shown that the measurements of the bearing angles between the robots are sufficient for reaching a balanced circular formation. We consider two different scenarios that the connectivity graph of the system is either a complete graph or a ring. Collision avoidance capabilities are added to the team members and the effectiveness of the control laws are demonstrated on a group of mobile robots. PublicationStable Flocking of Mobile Agents, Part II: Dynamic Topology(2003-12-09) Jadbabaie, Ali; Tanner, Herbert G; Pappas, George JThis is the second of a two-part paper, investigating the stability properties of a system of multiple mobile agents with double integrator dynamics. In this second part, we allow the topology of the control interconnections between the agents in the group to vary with time. Specifically, the control law of an agent depends on the state of a set of agents that are within a certain neighborhood around it. As the agents move around this set changes, giving rise to a dynamic control interconnection topology and a switching control law. This control law consists of a a combination of attractive/repulsive and alignment forces. The former ensure collision avoidance and cohesion of the group and the latter result to all agents attaining a common heading angle, exhibiting flocking motion. Despite the use of only local information and the time varying nature of agent interaction which affects the local controllers, flocking motion is established, as long as connectivity in the neighboring graph is maintained. PublicationOn the stability of unconstrained receding horizon control with a general terminal cost(2001-12-04) Jadbabaie, Ali; Hauser, JohnThis paper deals with unconstrained receding horizon control of nonlinear systems with a general, non-negative terminal cost. Earlier results have indicated that when the terminal cost is a suitable local control Lyapunov function, the receding horizon scheme is stabilizing for any horizon length. In a recent paper, the authors show that there always exist a uniform horizon length which guarantees stability of the receding horizon scheme over any sub-level set of the finite horizon cost when the terminal cost is identically zero. In this paper, we extend this result to the case where the terminal cost is a general non-negative function. PublicationDistributed Topology Control of Dynamic Networks(2008-06-11) Zavlanos, Michael M; Tahbaz-Salehi, Alireza; Jadbabaie, Ali; Pappas, George JIn this paper, we present a distributed control framework for controlling the topology of dynamic multi-agent networks. Agents are equipped with local sensing and wireless communication capabilities, however, due to power constraints, they are required to switch between two modes of operation, namely active and sleep. The control objective investigated in this paper is to determine distributed coordination protocols that regulate switching between the operation modes of every agent such that the overall network guarantees multi-hop communication links among a subset of so called boundary agents. In the proposed framework, coordination is based on a virtual market where every request to switch off is associated with a bid. Combinations of requests are verified with respect to connectivity and the one corresponding to the highest aggregate bid is finally served. Other than nearest neighbor information, our approach assumes no knowledge of the network topology, while verification of connectivity relies on notions of algebraic graph theory as well as gossip algorithms run over the network. Integration of the individual controllers results in an asynchronous networked control system for which we show that it satisfies the connectivity specification almost surely. We finally illustrate efficiency of our scalable approach in nontrivial computer simulations. PublicationDetermining interconnections in biochemical networks using linear programming(2008-12-09) August, Elias; Papachristodoulou, Antonius; Recht, Ben; Roberts, Mark; Jadbabaie, AliWe present a methodology for efficient, robust determination of the interaction topology of networked dynamical systems using time series data collected from experiments, under the assumption that these networks are sparse, i.e., have much less edges than the full graph with the same vertex set. To achieve this, we minimize the 1-norm of the decision variables while keeping the data in close Euler fit, thus putting more emphasis on determining the interconnection pattern rather than the closeness of fit. First, we consider a networked system in which the interconnection strength enters in an affine way in the system dynamics. We demonstrate the ability of our method to identify a network structure through numerical examples. Second, we extend our approach to the case of gene regulatory networks, in which the system dynamics are much more complicated. PublicationStable Flocking of Mobile Agents, Part I: Fixed Topology(2003-12-09) Jadbabaie, Ali; Tanner, Herbert G; Pappas, George JThis is the first of a two-part paper that investigates the stability properties of a system of multiple mobile agents with double integrator dynamics. In this first part we generate stable flocking motion for the group using a coordination control scheme which gives rise to smooth control laws for the agents. These control laws are a combination of attractive/repulsive and alignment forces, ensuring collision avoidance and cohesion of the group and an aggregate motion along a common heading direction. In this control scheme the topology of the control interconnections is fixed and time invariant. The control policy ensures that all agents eventually align with each other and have a common heading direction while at the same time avoid collisions and group into a tight formation.