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arXiv 2020年

作者： Jafarpour, Saber Velarde, Cisneros Bullo, Francesco Center of Control Dynamical Systems and Computation UC Santa Barbara CA93106-5070 United States

We develop two generalizations of contraction theory: semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix semi-measures, characterize their properties, and provide techniques to compute them. We also propose two optimization problems for the spectral abscissa of a given matrix using its semi-measures. For dynamical systems, we use the semi-measure of their Jacobian to study convergence of their trajectories to invariant subspaces. Second, we provide a comprehensive treatment of weakly-contracting systems;we prove a dichotomy for asymptotic behavior of their trajectories and show that, for their equilibrium points, local asymptotic stability implies global asymptotic stability. Third, we introduce the class of doubly-contracting systems and show that every trajectory of a doubly-contracting system converges to an equilibrium point. Finally, we apply our results to various important network systems including affine averaging and affine flow systems, continuous-time distributed primal-dual algorithms, and networks of diffusively-coupled oscillators. Copyright © 2020, The Authors. All rights reserved.

关键词： Trajectories

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Perspectives on Contractivity in control, Optimization, and Learning

arXiv

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arXiv 2024年

作者： Davydov, Alexander Bullo, Francesco The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States

Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction theory. These opinions are (i) contraction theory is a unifying framework emerging from classical and modern works, (ii) contractivity is computationally-friendly, robust, and modular stability, (iii) numerous dynamical systems are contracting, (iv) contraction theory is relevant to modern applications, and (v) contraction theory can be vastly extended in numerous directions. We survey recent theoretical and applied research in each of these five directions. Copyright © 2024, The Authors. All rights reserved.

关键词： System stability

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Formation control of autonomous robots based on cooperative behavior 10

Formation control of autonomous robots based on cooperative ...

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2009 10th European control Conference, ECC 2009

作者： Dorfler, Florian Francis, Bruce Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 United States Electrical and Computer Engineering Department University of Toronto TorontoM5S3G4 Canada

ISBN: (纸本)9783952417393

This paper considers the formation control problem for autonomous robots, where the target formation is specified as a minimally rigid formation. A distributed control law based on potential functions is derived from a directed sensor graph and relies on the graph matrices only. By methods of inverse optimality a certain class of sensor graphs is identified that is related to a cooperative behavior among the robots. These graphs are referred to as cooperative graphs, and undirected graphs, directed cycles, and directed open chain graphs can be identified as such graphs. Cooperative graphs admit a local stability result of the target formation together with a guaranteed region of attraction, that depends on the rigidity properties of the formation. © 2009 EUCA.

关键词： Robots

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Proximal Gradient Dynamics: Monotonicity, Exponential Convergence, and Applications

arXiv

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arXiv 2024年

作者： Gokhale, Anand Davydov, Alexander Bullo, Francesco The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States

In this letter we study the proximal gradient dynamics. This recently-proposed continuous-time dynamics solves optimization problems whose cost functions are separable into a nonsmooth convex and a smooth component. First, we show that the cost function decreases monotonically along the trajectories of the proximal gradient dynamics. We then introduce a new condition that guarantees exponential convergence of the cost function to its optimal value, and show that this condition implies the proximal Polyak-Lojasiewicz condition. We also show that the proximal Polyak-Lojasiewicz condition guarantees exponential convergence of the cost function. Moreover, we extend these results to time-varying optimization problems, providing bounds for equilibrium tracking. Finally, we discuss applications of these findings, including the LASSO problem, certain matrix based problems and a numerical experiment on a feed-forward neural network. Copyright © 2024, The Authors. All rights reserved.

关键词： Cost functions

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Modeling and Analysis of Competitive Propagation with Social Conversion

Modeling and Analysis of Competitive Propagation with Social...

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IEEE Annual Conference on Decision and control

作者： Wenjun Mei Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara Santa Barbara CA 93106 USA

ISBN: (纸本)9781467360890

In this paper we model a class of propagation processes for multiple competing products on a contact network and analyze the resulting dynamical behaviors. We assume three types of product-adoption processes for each individual: self adoption, social adoption and social conversion. On this basis, we build a Markov chain model of the competitive propagation process. Based on the independence approximation, a difference equations system, referred to as the network competitive propagation model, is derived to approximate the original Markov chain. Both simulation work and theoretical results are given to evaluate the accuracy of the independence approximation. The network competitive propagation model does not exclude the long-term coexistence of the mutually exclusive competing products spreading in a single-layer network. The result on coexistence is contrary to some previous literature on the propagation of multiple memes. Moreover, we find that the probability distributions of nodes' states achieve asymptotic consensus, which indicates that our network competitive propagation model is a good example of network dynamics with both consensus and propagation behaviors. Theoretical analysis also reveals that, the rate of convergence to the consensus value depends on the self-adoption process, social conversion process, as well as the network topology.

关键词： Markov chain propagation process Network topology Probability distribution Contact networks Modeling Coexistence Network

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Dynamic Vehicle Routing with Moving Demands - Part I: Low speed demands and high arrival rates

Dynamic Vehicle Routing with Moving Demands - Part I: Low sp...

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2009 American control Conference (ACC 2009)

作者： Shaunak D. Bopardikar Stephen L. Smith Francesco Bullo Joao P. Hespanha Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106 USA

ISBN: (纸本)9781424445233

We introduce a dynamic vehicle routing problem in which demands arrive uniformly on a segment and via a temporal Poisson process. Upon arrival, the demands translate perpendicular to the segment in a given direction and with a fixed speed. A service vehicle, with speed greater than that of the demands, seeks to serve these translating demands. For the existence of any stabilizing policy, we determine a necessary condition on the arrival rate of the demands in terms of the problem parameters: (i) the speed ratio between the demand and service vehicle, and (ii) the length of the segment on which demands arrive. Next, we propose a novel policy for the vehicle that involves servicing the outstanding demands as per a translational minimum Hamiltonian path (TMHP) through the moving demands. We derive a sufficient condition on the arrival rate of the demands for stability of the TMHP-based policy, in terms of the problem parameters. We show that in the limiting case in which the demands move much slower than the service vehicle, the necessary and the sufficient conditions on the arrival rate are within a constant factor.

关键词： Vehicle dynamics Routing Unmanned aerial vehicles Stability Sufficient conditions Marine vehicles Robotics and automation Surveillance Defense industry Belts

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Uniting local and global output feedback controllers

Uniting local and global output feedback controllers

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作者： Prieur, Christophe Teel, Andrew R. LAAS-CNRS 7 Avenue du Colonel Roche 31077 Toulouse Cedex 4 France Center for Control Dynamical Systems and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA 93106-9560 United States

ISBN: (纸本)9783902661289

We consider control systems for which we know two stabilizing output feedback controllers. One is globally asymptotically stabilizing, while the other one is only locally asymptotically stabilizing. We look for a composite output feedback control law that is equal to the local feedback on a neighborhood of the origin and that is globally asymptotically stabilizing. We insist on using only output feedback controllers to solve this uniting problem. Since we want some robustness with respect to measurement noise, actuator errors and external disturbances, we consider hybrid output feedback controllers, following recent developments in the literature on robustness in hybrid systems. Under an input-output-to-state stability assumption, we exhibit a solution of this uniting problem by means of a dynamic hybrid output feedback controller. Copyright © 2007 IFAC.

关键词： Hybrid systems

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Algorithms for regional source localization

Algorithms for regional source localization

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2009 American control Conference (ACC 2009)

作者： Sandra H. Dandach Francesco Bullo Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106 USA

ISBN: (纸本)9781424445233

In this paper we use the MAP criterion to locate a region containing a source. Sensors placed in a field of interest divide the latter into smaller regions and take measurements that are transmitted over noisy wireless channels. We propose implementations of our algorithm that consider complete and limited communication among sensors and seek to choose the most likely hypothesis. Each hypothesis corresponds to the event that a given region contains the source. Corrupted measurements are used to calculate conditional posteriors. We prove that the algorithms asymptotically find the correct region almost surely as long as information is available from three or more sensors. We also study the geometric properties of the model that make it possible in some situations to detect the correct region with a unique sensor. Our simulations confirm that the performance of algorithms with complete and limited information improves with decreasing noise.

关键词： Propagation losses Convergence Partitioning algorithms Sensor phenomena and characterization Decision making Wireless sensor networks Solid modeling Linear approximation Sufficient conditions Algorithm design and analysis

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Pairwise optimal discrete coverage control for gossiping robots

Pairwise optimal discrete coverage control for gossiping rob...

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IEEE Conference on Decision and control

作者： Joseph W. Durham Ruggero Carli Francesco Bullo Center of Control Dynamical Systems and Computation University of California슠Santa Barbara Santa Barbara CA USA

ISBN: (纸本)9781424477456

We propose distributed algorithms to automatically deploy a group of robotic agents and provide coverage of a discretized environment represented by a graph. The classic Lloyd approach to coverage optimization involves separate centering and partitioning steps and converges to the set of centroidal Voronoi partitions. In this work we present a novel graph coverage algorithm which achieves better performance without this separation while requiring only pairwise “gossip” communication between agents. Our new algorithm provably converges to an element of the set of pairwise-optimal partitions, a subset of the set of centroidal Voronoi partitions. We illustrate that this new equilibrium set represents a significant performance improvement through numerical comparisons to existing Lloyd-type methods. Finally, we discuss ways to efficiently do the necessary computations.

关键词： Partitioning algorithms Robot kinematics Optimization Stochastic processes Convergence Heuristic algorithms

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Contractivity of the Method of Successive Approximations for Optimal control

arXiv

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arXiv 2022年

作者： Smith, Kevin D. Bullo, Francesco Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93101 United States

Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications (e.g., in controls and learning), and their study is receiving increasing attention. This work starts with the simple observation that, given a strongly contracting system, its adjoint dynamical system is also strongly contracting, with the same rate, with respect to the dual norm, under time reversal. As main implication of this dual contractivity, we show that the classic Method of Successive Approximations (MSA), an indirect method in optimal control, is a contraction mapping for short optimization intervals or large contraction rates. Consequently, we establish new convergence conditions for the MSA algorithm, which further imply uniqueness of the optimal control and sufficiency of Pontryagin’s minimum principle under additional assumptions. Copyright © 2022, The Authors. All rights reserved.

关键词： dynamical systems

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