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作者： Bürger, Mathias Notarstefano, Giuseppe Allgöwer, Frank Bullo, Francesco Institute for Systems Theory and Automatic Control University of Stuttgart Pfaffenwaldring 9 70550 Stuttgart Germany Department of Engineering University of Lecce Via per Monteroni 73100 Lecce Italy Center for Control Dynamical Systems and Computation University of California Santa Barbara CA 93106 United States

ISBN: (纸本)9781457700804

In this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous networks. Namely, we propose a distributed version of the well known simplex algorithm. We prove its convergence to the global lexicographic minimum for possibly fully degenerate problems and provide simulations supporting the conjecture that the completion time scales linearly with the diameter of the graph. The algorithm can be interpreted as a dual version of the constraints consensus algorithm proposed in [1] to solve abstract programs when the last is applied to linear programs. Finally, we study a multi-agent task assignment problem and show that it can be solved by means of our distributed simplex algorithm. © 2011 AACC American Automatic control Council.

关键词： Linear programming

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A distributed algorithm for random convex programming

A distributed algorithm for random convex programming

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International Conference on NETwork Games, control and Optimization, NetGCooP 2011

作者： Carlone, Luca Srivastava, Vaibhav Bullo, Francesco Calafiore, Giuseppe C. Laboratorio di Meccatronica Politecnico di Torino Italy Center for Control Dynamical Systems and Computation University of California Santa Barbara CA United States Dipartimento di Automatica e Informatica Politecnico di Torino Italy

ISBN: (纸本)9781467303842

We study a distributed approach for solving random convex programs (RCP) for the case in which problem constraints are distributed among nodes in a processor network. We devise a distributed algorithm that allows network nodes to reach consensus on problem solution by exchanging a local set of constraints at each iteration. We prove that the algorithm assures finite-time convergence to problem solution and we provide explicit bounds on the maximum number of constraints to be exchanged among nodes at each communication round. Numerical experiments confirm the theoretical derivation and show that a parallel implementation of the proposed approach speeds-up the solution of the RCP with respect to centralized computation. © 2011 INRIA.

关键词： Convex optimization

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Topological Equivalence of a Structure-Preserving Power Network Model and a Non-Uniform Kuramoto Model of Coupled Oscillators

Topological Equivalence of a Structure-Preserving Power Netw...

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IEEE Conference on Decision and control

作者： Florian Dorfler Francesco Bullo Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106

ISBN: (纸本)9781612848006

We study synchronization in the classic structure-preserving power network model proposed by Bergen and Hill. We find that, locally near the synchronization manifold, the phase and frequency dynamics of the power network model are topologically conjugate to the phase dynamics of a non-uniform Kuramoto model together with decoupled and stable frequency dynamics. This topological conjugacy implies the equivalence of local synchronization in power networks and in non-uniform Kuramoto oscillators. Hence, we can harness the results available for Kuramoto oscillators to analyze synchronization in power networks. We establish necessary and sufficient conditions for phase synchronization, sufficient conditions for frequency synchronization, and necessary and sufficient conditions for frequency synchronization with a uniform topology. These conditions also extend the results known for the classic first-order Kuramoto model and second-order consensus protocols. Our conditions all share a common physical interpretation: the non-uniformity between real power injections has be compensated by sufficiently strong coupling.

关键词： Synchronization Frequency synchronization Mathematical model Stability analysis Power system stability Couplings Power system dynamics

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Model Selection in Stochastic Chemical Reaction Networks Using Flow Cytometry Data

Model Selection in Stochastic Chemical Reaction Networks Usi...

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IEEE Conference on Decision and control

作者： Gabriele Lillacci Mustafa Khammash Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA USA

ISBN: (纸本)9781612848006

The model selection problem, that is picking the model that best explains an experimental data set from a list of candidates, arises frequently when studying unknown biological processes. Here, we propose a new method for model selection in stochastic chemical reaction networks using measurements from flow cytometry. A distinctive feature of our approach is its ability to perform statistically significant selection using a very small number of Monte Carlo simulations of the candidate stochastic models. After a comprehensive review of the theory associated with our procedure, we describe the model selection algorithm and we demonstrate it on an example drawn from molecular biology.

关键词： model selection Monte Carlo technique Flow Cytometry selection algorithm Stochastic molecular biology

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Stochastic surveillance strategies for spatial quickest detection

Stochastic surveillance strategies for spatial quickest dete...

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IEEE Conference on Decision and control

作者： Vaibhav Srivastava Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara Santa Barbara CA USA

ISBN: (纸本)9781612848006;9781612848013

We present stochastic vehicle routing policies for detection of any number of anomalies in a set of regions of interest. The autonomous vehicle collects information from a set of regions and sends it to a fusion center. The vehicle follows a randomized region selection policy at each iteration. Using the collected information, the fusion center runs an ensemble of cumulative sum (CUSUM) algorithms in order to detect the presence of an anomaly in any region. We first determine optimal stationary policies that result in quickest detection of all anomalies. We then study an adaptive policy that assigns higher selection probability to a region with higher likelihood of an anomaly. We provide a comparative study of these policies.

关键词： Routing Delay Probability Surveillance Vehicles Optimization Humans

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On the Critical Coupling Strength for Kuramoto Oscillators

On the Critical Coupling Strength for Kuramoto Oscillators

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2011 American control Conference (ACC)

作者： Florian Dorfler Francesco Bullo Center for Control Dynamical Systems and Computation University of California슠Santa Barbara Santa Barbara CA USA

The celebrated Kuramoto model captures various synchronization phenomena in biological and man-made dynamical systems of coupled oscillators. It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency to synchronization occurs. This paper features three contributions. First, we characterize and distinguish the different notions of synchronization used throughout the literature and formally introduce the concept of phase cohesiveness as an analysis tool and performance index for synchronization. Second, we review the vast literature providing necessary, sufficient, implicit, and explicit estimates of the critical coupling strength in the finite and infinite-dimensional case. Finally, we present the first explicit necessary and sufficient condition on the critical coupling strength to achieve synchronization in the finite-dimensional Kuramoto model for an arbitrary distribution of the natural frequencies. The multiplicative gap in the synchronization condition yields a practical stability result determining the admissible initial and the guaranteed ultimate phase cohesiveness as well as the guaranteed asymptotic magnitude of the order parameter.

关键词： Synchronization Couplings Oscillators Frequency synchronization Stability analysis Mathematical model Trajectory

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Hybrid Combinatorial Optimization: Sample Problems and Algorithms

Hybrid Combinatorial Optimization: Sample Problems and Algor...

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IEEE Conference on Decision and control

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

ISBN: (纸本)9781612848006

We study a class of non-convex optimization problems involving sigmoid functions. We show that sigmoid functions impart a combinatorial element to the optimization variables and make them hybrid of continuous and discrete variables. We formulate versions of the knapsack problem and the bin-packing problem with such hybrid variables. We utilize the approximation algorithms from the combinatorial optimization literature and develop approximation algorithms for these NP-hard hybrid optimization problems.

关键词： Resource management Approximation algorithms Optimization Approximation methods Humans Equations Algorithm design and analysis

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Stochastic strategies for survival: bacterial competence in Bacillus Subtilis

Stochastic strategies for survival: bacterial competence in ...

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2011 American control Conference (ACC)

作者： Sandra H. Dandach Mustafa Khammash Center for Control Dynamical Systems and Computation University of California슠Santa Barbara Santa Barbara CA USA

Under stressful environments, organisms take actions that help them protect their DNA. An example of such actions is the stochastic switching that Bacillus subtilis undergoes, in which it goes from the vegetative state to a competent state. When in competence, the cell has an increased ability to bind to and internalize exogenous DNA. This increases the chances of survival of a cell. Competence is nonetheless an expensive state for the cell to be in, so the decision to switch undergoes a very delicate regulation. A major player in controlling the switching of the cell is the ComK protein. ComK protein is a key regulator which activates hundreds of genes, including the genes encoding the DNA-uptake and recombination systems. In Bacillus subtilis, stress in the environment activates a sequence of chemical reactions that, driven by cellular noise, stochastically increases the level of ComK in some bacterial cells driving them from their original vegetative state into a competent state. In this work, we use the Finite State Projection (FSP) method to analyze stochastic biochemical events and to study the excitable dynamics responsible for competence in Bacillus Subtilis. We compute the probability with which Bacillus subtilis enters in competence. We also present a method to analyze the sensitivity of these stochastic events to various system parameters such as binding affinities, transcription rates, degradation rates, etc.

关键词： Mathematical model Integrated circuit modeling Numerical models Stochastic processes Equations Sensitivity Chemicals

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Hide-and-Seek with Directional Sensing *

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IFAC Proceedings Volumes 2011年第1期44卷 9343-9348页

作者： Alessandro Borri Shaunak D. Bopardikar Joao P. Hespanha Maria D. Di Benedetto Department of Electrical Engineering University of L'Aquila Italy Center for Control Dynamical Systems and Computation University of California at Santa Barbara CA 93106 USA

Abstract We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a mobile agent, and whenever it physically visits a sensor, the sensor returns a random direction, corresponding to a half-plane in which the hidden object is located. We first present a novel search heuristic and characterize bounds on the expected distance covered before reaching the object. Next, we model this game as a large-dimensional zero-sum dynamic game and we apply a recently introduced randomized sampling technique that provides a probabilistic level of security to the hider. We observe that, when the randomized sampling approach is only allowed to select a very small number of samples, the cost of the heuristic is comparable to the security level provided by the randomized procedure. However, as we allow the number of samples to increase, the randomized procedure provides a higher probabilistic security level.

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On Opinion Dynamics in Heterogeneous Networks

On Opinion Dynamics in Heterogeneous Networks

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2011 American control Conference (ACC)

作者： Anahita Mirtabatabaei Francesco Bullo Center for Control Dynamical Systems and Computation University of California슠Santa Barbara Santa Barbara CA USA

This paper studies the opinion dynamics model recently introduced by Hegselmann and Krause: each agent in a group maintains a real number describing its opinion;and each agent updates its opinion by averaging all other opinions that are within some given confidence range. The confidence ranges are distinct for each agent. This heterogeneity and state-dependent topology leads to poorly-understood complex dynamic behavior. We classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. We conjecture that any trajectory of this model eventually converges to a steady state under fixed topology. To establish this conjecture, we derive two novel sufficient conditions: both conditions guarantee convergence and constant topology for infinite time, while one condition also guarantees monotonicity of the convergence. In the evolution under fixed topology for infinite time, we define leader groups that determine the followers' rate and direction of convergence.

关键词： Convergence Topology Trajectory Network topology computational modeling Steady-state Mathematical model

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