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

ISBN: (纸本)9781424474264

Motivated by recent interest for multi-agent systems and smart grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a non-uniform Kuramoto model characterized by multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. By extending methods from synchronization theory and consensus protocols, we establish sufficient conditions for synchronization of non-uniform Kuramoto oscillators. These conditions reduce to and improve upon previously-available tests for the classic Kuramoto model. By combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying network parameters and initial conditions. © 2010 AACC.

关键词： Synchronization

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Distributed estimation and detection under local information

Distributed estimation and detection under local information

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作者： Pasqualetti, F. Carli, R. Bicchi, A. Bullo, F. Center for Control Dynamical Systems and Computation University of California Santa Barbara United States Centro I. R. E. Piaggio Università di Pisa Pisa Italy

ISBN: (纸本)9783902661821

This work considers the problem of obtaining optimal estimates via distributed computation in a large scale system. The electric power system, the transportation system, and generally any computer or network system, are examples of large scale systems: a decentralized estimation of signals based on observations acquired by spatially distributed sensors is the basis for a wide range of important applications. In this work, we focus on the problem of reconstructing the initial state of a linear network in the presence of process and measurement noise. We consider a local model information setup, in which the entire dynamical and measurement model is nowhere available and cannot be reconstructed for the computation. Our estimation procedure relies upon a novel technique to solve a consistent system of linear equations, for which we prove correctness and convergence. In the second part of the paper we consider the problem of detecting anomalies in a large scale network driven by noise. Despite the theoretical advances in this field of research, the currently available procedures to enforce security in large scale systems are computationally inefficient and numerically unreliable. Using our optimal estimation scheme, we describe a distributed procedure with performance guarantees that only requires local knowledge of the system model. © 2010 IFAC.

关键词： Electric power systems

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Synchronization of Power Networks: Network Reduction and Effective Resistance

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IFAC Proceedings Volumes 2010年第19期43卷 197-202页

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

In transient stability studies in power networks two types of mathematical models are commonly used – the differential-algebraic structure-preserving model and the reduced dynamic model of interconnected swing equations. This paper analyzes the reduction process relating the two power network models. The reduced admittance matrix is obtained by a Schur complement of the topological network admittance matrix with respect to its bus nodes. We provide a detailed spectral, algebraic, and graph-theoretic analysis of this network reduction process, termed Kron reduction, with particular focus on the effective resistance. As an application of this analysis, we are able to state concise conditions relating synchronization in the considered structure-preserving power network model directly to the state, parameters, and topology of the underlying network. In particular, we provide a spectral condition based on the algebraic connectivity of the network and a second condition based on the effective resistance among generators.

关键词： transient stability synchronization structure-preserving power network model

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Construction of Lyapunov Functions for Piecewise-Deterministic Markov Processes

Construction of Lyapunov Functions for Piecewise-Determinist...

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2010 49th IEEE Conference on Decision and control

作者： Alexandre R. Mesquita Joao P. Hespanha Center for Control Dynamical Systems and Computation University of California Santa Barbara CA 93106

ISBN: (纸本)9781424477456

The purpose of this contribution is twofold: 1) to present for the first time a Lyapunov function that proves exponential ergodicity of a process studied by the authors in [1], where the problem of controlling the probability density of a swarm of robotic agents was solved;2) to introduce alongside the method used to construct this Lyapunov function, which is of interest in its own since it may be applicable to a wide class of piecewise-deterministc Markov processes. Our method searches for the Lyapunov function that maximizes a measure of the rate of convergence that appears in the theory of large deviations. Analytical solutions are often possible as shown by examples.

关键词： Liapunov function Markov chain dike swarms

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Vehicle placement to intercept moving targets

Vehicle placement to intercept moving targets

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作者： Bopardikar, Shaunak D. Smith, Stephen L. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106 United States Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology Cambridge MA 02139 United States

ISBN: (纸本)9781424474264

We address optimal placement of vehicles with simple motion, to intercept a mobile target that arrives stochastically on a line segment. The optimality of vehicle placement is measured through a cost function associated with intercepting the target. With a single vehicle, we assume that the target either moves with fixed speed and in a fixed direction or moves to maximize the vertical height or intercept time. We show that each of the corresponding cost functions is convex, has smooth gradient and has a unique minimizing location, and so the optimal vehicle placement is obtained by any standard gradient-based optimization technique. With multiple vehicles, we assume that the target moves with fixed speed and in fixed direction. We present a discrete time partitioning and gradientbased algorithm, and characterize conditions under which the algorithm asymptotically leads the vehicles to a set of critical configurations of the cost function. © 2010 AACC.

关键词： Vehicles

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Parameter Identification of Biological Networks Using Extended Kalman Filtering and (chi)~(2) Criteria

Parameter Identification of Biological Networks Using Extend...

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2010 49th 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)9781424477456

Parameter estimation is a central issue in systems biology, as it represents the key step in obtaining information from computational models of biological systems. The extended Kalman filter (EKF) in its various implementations has been proposed as a parameter estimator by several authors. However, in many cases, and in particular when the estimation problem involves a large number of unknown parameters, the EKF can perform poorly. In this paper we show how the knowledge of the statistics of the measurement noise can be used to validate or invalidate the estimates provided by the filter, and to refine them in case they turn out not to be satisfactory. We demonstrate these ideas on a simple gene expression model, and we show how the proposed method offer advantages over classical techniques such as least-squares estimation.

关键词： Parameter identification extended Kalman filtering Noise measurement Extended Kalman filters computational modeling systems biology Parameter estimation Filters Unknown parameter

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Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators

Synchronization and Transient Stability in Power Networks an...

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American control Conference

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)9781424474264

关键词： Oscillators Power system modeling Power system transients Power system stability Multiagent systems Smart grids Power system analysis computing Character generation Equations Protocols

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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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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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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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