Jadbabaie, Ali
Email Address
ORCID
Disciplines
relationships.isProjectOf
relationships.isOrgUnitOf
Position
Introduction
Research Interests
Collection
33 results
Search Results
Now showing 1 - 10 of 33
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 Vision-Based, Distributed Control Laws for Motion Coordination of Nonholonomic Robots(2009-08-01) Moshtagh, Nima; Michael, Nathan D; Jadbabaie, Ali; Daniilidis, KostasIn this paper, we study the problem of distributed motion coordination among a group of nonholonomic ground robots. We develop vision-based control laws for parallel and balanced circular formations using a consensus approach. The proposed control laws are distributed in the sense that they require information only from neighboring robots. Furthermore, the control laws are coordinate-free and do not rely on measurement or communication of heading information among neighbors but instead require measurements of bearing, optical flow, and time to collision, all of which can be measured using visual sensors. Collision-avoidance capabilities are added to the team members, and the effectiveness of the control laws are demonstrated on a group of mobile robots.Publication Consensus 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 [1] is a special case of the model proposed in this paper.Publication Game Theoretic Analysis of a Strategic Model of Competitive Contagion and Product Adoption in Social Networks(2012-12-01) Fazeli, Arastoo; Jadbabaie, AliIn this paper we propose and study a strategic model of marketing and product adoption in social networks. Two firms compete for the spread of their products in a social network. Considering their fixed budgets, they initially determine the payoff of their products and the number of their initial seeds in a network. Afterwards, neighboring agents play a local coordination game over a fixed network which determines the dynamics of the spreading. Assuming myopic best response dynamics, agents 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 find a lower and an upper bound on the proportion of product adoptions. We derive an explicit characterization of these bounds based on the payoff of products offered by firms, the initial number of adoptions and the underlying structure of the network. We then consider a case in which after switching to the new product, agents might later switch back to the old product with some fixed rate. We show that depending on the rate of switching back to the old product, the new product might always die out in the network eventually. Finally, we consider a game between two firms aiming to optimize their products adoptions while considering their fixed budgets. We describe the Nash equilibrium of this game and show how the optimal payoffs offered by firms and the initial number of seeds depend on the relative budgets of firms.Publication 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.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 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 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 Aggressive maneuvering of a thrust vectored flying wing: A receding horizon approach(2000-12-12) Hauser, John; Jadbabaie, AliThis paper deals with the control of a thrust vectored flying wing known as the ducted fan, developed at California Institute of Technology. The experiment was developed to serve as a testbed for nonlinear control design. In an earlier paper, the authors reported simulation results based on a simplified (no aerodynamics involved) planar model of the ducted fan around hover position. In this paper we report on the modeling and simulation of the ducted fan in forward flight, where aerodynamic forces and moments can no longer be ignored. A receding horizon scheme is developed to generate trajectories for the forward flight model. Using a more simplified version of the model, some aggressive trajectories are generated. These trajectories are then used as a reference in the receding horizon scheme, and morphed into the trajectories of the full model. Simulation results depict the capabilities of the ducted fan as well as this methodology in performing aggressive maneuvers.