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arXiv 2023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 distributed optimization and Nash equilibrium-seeking dynamics from a contraction theoretic perspective. Our first result is a novel bound on the logarithmic norm of saddle matrices. Second, for distributed gradient flows based upon incidence and Laplacian constraints over arbitrary topologies, we establish strong contractivity over an appropriate invariant vector subspace. Third, we give sufficient conditions for strong contractivity in pseudogradient and best response games with complete information, show the equivalence of these conditions, and consider the special case of aggregative games. Copyright © 2023, The Authors. All rights reserved.

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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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Accuracy and Decision Time for Decentralized Implementations of the Sequential Probability Ratio Test

Accuracy and Decision Time for Decentralized Implementations...

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American control Conference

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

ISBN: (纸本)9781424474264

This paper focuses on decentralized decision making in a population of individuals each implementing the sequential probability ratio test. The individual decisions are combined by a fusion center into a collective decision via an aggregation rule. For distinct aggregation rules, we study how the population size affects the performance of the collective decision making, i.e., the decision accuracy and time. We analyze two aggregation rules, the fastest rule and the majority rule. In the fastest rule, the group decision is equal to the first decision made by any individual. In the majority rule, the group decision is equal to the majority of the decisions. Under the assumption of measurement independence among individuals, we introduce a novel numerical representation of the performance of decentralized decision making. We study our settings analytically as well as numerically. Our numerical results and simulations characterize the tradeoff between accuracy and decision time as a function of the population size.

关键词： Sequential analysis Decision making Delta modulation Numerical simulation History Bayesian methods Social network services Voting control systems Performance analysis

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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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A cooperative Homicidal Chauffeur game

A cooperative Homicidal Chauffeur game

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Proceedings of the 46th IEEE Conference on Decision and control, Pages 1383-1838

作者： Shaunak D. Bopardikar Francesco Bullo Joao Hespanha Center for Control Dynamical systems and Computation University of California슠Santa Barbara Santa Barbara CA USA

ISBN: (纸本)9781424414970;1424414970

We address a pursuit-evasion problem involving an unbounded planar environment, a single evader, and multiple pursuers moving along curves of bounded curvature. The problem amounts to a multi-agent version of the classic homicidal chauffeur problem;we focus on parameter ranges in which a single pursuer is not sufficient to capture the evader. We propose a novel cooperative strategy in which the pursuers move in a daisy-chain formation and confine the evader to a bounded region. The proposed policy is inspired by certain hunting and foraging behaviors of various fish species. We characterize the required number of pursuers and the required value of the evader/pursuers speed ratio for which our strategy is guaranteed to lead to confinement.

关键词： Chauffeurs Hunting Game theory Game animals Bounded

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Accuracy and Decision Time for a Class of Sequential Decision Aggregation Rules

Accuracy and Decision Time for a Class of Sequential Decisio...

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2010 49th IEEE Conference on Decision and control

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

ISBN: (纸本)9781424477456

This work focuses on decentralized decision making in a population of individuals each implementing the sequential probability ratio test. The individual decisions are combined into a decentralized decision via an aggregation rule chosen from a family of aggregation rules, denoted as q out of N rule. We study how the population size affects the performance of the decentralized decision making, i.e., the decision accuracy and time. In a group applying the q ouf of N, a global decision is reached as soon as q out of the N decision makers agree on an answer. Under the assumption of measurement independence among individuals, we introduce a novel numerical method that allows the analysis of the decision accuracy and time of a group of decision makers. We present the numerical method and show a preliminary sets of results that can be obtained using such a method.

关键词： decision makers Numerical methods Decentralized sprt population size Rule

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Enforced symmetry of the stance phase for the Spring-Loaded Inverted Pendulum

Enforced symmetry of the stance phase for the Spring-Loaded ...

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IEEE International Conference on Robotics and Automation (ICRA)

作者： Giulia Piovan Katie Byl Center for Control Dynamical Systems and Computation University of California슠Santa Barbara Santa Barbara CA USA

The Spring-Loaded Inverted Pendulum (SLIP) is considered the simplest model to effectively describe bouncing gaits (such as running and hopping) for many legged animals and robots. For this reason, it is has often been used as a model for robot design. A key challenge in using this model, however, is the lack of a closed-form solution for the equations of motion that define the stance phase of its dynamics. This results in the impossibility of analytically predicting its trajectory. Consequently, developing a practical control strategy to operate on the model is computationally intensive, because accurately predicting the step-to-step dynamics is still an unsolved problem. By adding an actuator in series with the spring, we can develop a control law for actuator displacement which enforces a desired trajectory during stance. In particular, for our specific chosen control law, we can compute an analytical solution for the stance phase trajectory. Furthermore, we give examples of higher level control strategies for foothold placement and for keeping the forward velocity or the apex height constant on rough terrain that employ our low-level control laws, and we illustrate through simulations the performance typical of our strategy.

关键词： Trajectory Actuators Springs Mathematical model computational modeling Equations Legged locomotion

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Stabilization of Networked control systems with Clock Offsets

Stabilization of Networked Control Systems with Clock Offset...

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American control Conference

作者： Masashi Wakaiki Kunihisa Okano Joao P. Hespanha Center for Control Dynamical-systems and Computation (CCDC) University of California Santa Barbara CA 93106-9560 USA

ISBN: (纸本)9781479917730

We consider the stabilization of networked control systems with time-invariant clock offsets between the sensors and the controllers. Clock offsets are modeled as parametric uncertainty and we provide necessary and sufficient conditions for the existence of a single controller that is capable of stabilizing the closed loop for every clock offset in a given range. For scalar systems, we obtain the maximum length of the offset interval for which the system can be stabilized by a single linear time-invariant controller. We compare the offset bounds that would be allowed by specific classes of controllers for scalar systems.

关键词： Networked control systems offsets Timing devices controllers clock skew maximum length control systems Signal controller time-invariant system clock

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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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