Jadbabaie, Ali
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Publication Effects 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.Publication Distributed 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.Publication Determining 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.Publication Stable 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.Publication Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules(2003-06-01) Jadbabaie, Ali; Lin, Jie; Morse, A. StephenIn a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent’s heading is updated using a local rule based on the average of its own heading plus the headings of its “neighbors.” In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent’s set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.Publication Elastic Multi-Particle Systems for Bounded-Curvature Path Planning(2008-06-11) Ahmadzadeh, Ali; Jadbabaie, Ali; Pappas, George J; Kumar, VijayThis paper investigates a path planning algorithm for Dubins vehicles. Our approach is based on approximation of the trajectories of vehicles using sequence of waypoints and treating each way point as a moving particle in the space. We define interaction forces between the particles such that the resulting multi-particle system will be stable, moreover, the trajectories generated by the waypoints in the equilibria of the multi-particle system will satisfy all of the hard constraint such as bounded-curvature constraint and obstacle avoidance.Publication Distributed Quadratic Programming over Arbitrary Graphs(2007-01-01) Motee, Nader; Jadbabaie, AliIn this paper, the locality features of infinitedimensional quadratic programming (QP) optimization problems are studied. Our approach is based on tools from operator theory and ideas from Multi Parametric Quadratic Programming (MPQP). The key idea is to use the spatially decaying operators (SD), which has been recently developed to study spatially distributed systems in [1], to capture couplings between optimization variables in the quadratic cost functional and linear constraints. As an application, it is shown that the problem of receding horizon control of spatially distributed systems with heterogeneous subsystems, input and state constraints, and arbitrary interconnection topologies can be modeled as an infinitedimensional QP problem. Furthermore, we prove that for a convex infinite-dimensional QP in which the couplings are through SD operators, optimal solution is piece-wise affine– represented as convolution sums. More importantly, we prove that the kernel of each convolution sum decays in the spatial domain at a rate proportional to the inverse of the corresponding coupling function of the optimization problem, thereby providing evidence that even centralized solutions to the infinite-dimensional QP has inherent spatial locality.Publication A Globally Stabilizing Receding Horizon Controller for Neutrally Stable Linear Systems with Input Constraints(2002-12-10) Jadbabaie, Ali; De Persis, Claudio; Yoon, Tae-WoongIt is well known that exponentially unstable linear systems can not be globally stabilized in the presence of input constraints. In the case where the linear system is neutrally stable, one can achieve global asymptotic stability using a particular control Lyapunov function (CLF)-based controller. Using this particular CLF as terminal cost in a receding horizon scheme, we obtain a receding horizon controller which globally stabilizes such systems. Contrary to previous results, the horizon length is fixed, and can be chosen arbitrarily. The resulting controller also outperforms the CLF controller, since it provides a lower cost as measured by a quadratic performance index.Publication Density Functions for Navigation Function Based Systems(2006-12-15) Loizou, Savvas G; Jadbabaie, AliIn this paper, we present a scheme for constructing density functions for systems that are almost globally asymptotically stable (i.e., systems for which all trajectories converge to an equilibrium except for a set of measure zero) based on navigation functions. Although recently-proven converse theorems guarantee the existence of density functions for such systems, results are only existential and the construction of a density function for almost globally asymptotically stable systems remains a challenging task. We show that for a specific class of dynamical systems that are defined based on a navigation function, a density function can be easily derived from the system's underlying navigation functionPublication Distributed coverage verification in sensor networks without location information(2008-12-09) 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.