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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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Online Optimal Switching of Single Phase DC/AC Inverters using Partial Information

Online Optimal Switching of Single Phase DC/AC Inverters usi...

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American control Conference

作者： Kyriakos G. Vamvoudakis Joao P. Hespanha Center for Control Dynamical-systems and Computation (CCDC) University of California Santa Barbara CA 93106-9560 USA

ISBN: (纸本)9781479932757

This paper proposes an online optimal tracking algorithm to provide the desired voltage magnitude and frequency at the load. This eventually will work as a DC/AC inverter that with appropriate switching of semiconductor devices will convert low DC voltage to high AC voltage. An L - C filter is used to reduce the effects caused by switching semiconductor devices. The proposed control scheme ensures a good tracking of an exosystem that provides the desired voltage magnitude and frequency. It builds upon the ideas of approximate dynamic programming (ADP) and uses only partial information of the system and exosystem. A Lyapunov stability proof ensures that the closed-loop system is asympotically stable. Finally, simulations show the effectiveness of the proposed approach.

关键词： Power systems voltage source inverter approximate dynamic programming voltage source inverter power systems voltage magnitude dynamic programming Semiconductor devices VOLTS DIRECT CURRENT Inventors Computer based information systems VOLTS ALTERNATING CURRENT switching Closed loop systems single phase

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On the Reflected Appraisals Dynamics of Influence Networks with Stubborn Agents

On the Reflected Appraisals Dynamics of Influence Networks w...

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American control Conference

作者： Anahita Mirtabatabaei Peng Jia Noah E. Friedkin Francesco Bullo Department of Mechanical Engineering and the Center for Control Dynamical Systems and Computation University of California at Santa Barbara Department of Sociology University of California at Santa Barbara

ISBN: (纸本)9781479932757

This article focuses on the evolution of interpersonal influences in a group of stubborn individuals as they discuss a sequence of issues. Each individual opinion about a single issue is updated based upon the convex combination of the individual's current opinion, the neighbors' current opinion, and the individual's initial opinion;the attachment to the initial opinion characterizes how stubborn an individual is. To model the evolution of the influence network, we employ Friedkin's "reflected appraisal" model: each individual's self-weight on a new issue is determined by the individual's average influence and relative control on other individuals on prior issue outcomes. These modeling assumptions lead to a dynamical system for the evolution of self-weights. We establish the well-posedness and continuity of the proposed dynamics and prove the existence and uniqueness of equilibria for stubborn individuals. We then study the impact of network topology on the individuals' final self-weights. We prove the convergence of all system trajectories for the special case of doubly-stochastic networks and homogeneous stubbornness. We characterize equilibrium self-weights for systems with centralized networks and heterogeneous stubbornness. Finally, our numerical simulations illustrate how existence, uniqueness and attractivity of the equilibria holds true for general network topologies and stubbornness values.

关键词： Vectors Equations Peer-to-peer computing Eigenvalues and eigenfunctions Topology Appraisal Network topology

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Hybrid systems with Memory: Modelling and Stability Analysis via Generalized Solutions

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IFAC Proceedings Volumes 2014年第3期47卷 6019-6024页

作者： Jun Liu Andrew R. Teel Department of Automatic Control and Systems Engineering University of Sheffield Sheffield S1 3JD United Kingdom Center for Control Dynamical Systems and Computation and Department of Electrical and Computer Engineering University of California Santa Barbara CA 93106 USA

Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. We present a general modelling framework for such systems using hybrid functional inclusions, whose generalized solutions are defined on hybrid time domains and evolve in the phase space of hybrid memory arcs equipped with the graphical convergence topology. We prove a general existence result based on some basic conditions on the data of hybrid systems. We further establish sufficient conditions for the stability analysis of hybrid systems with memory using Lyapunov-Razumikhin (L-R) functions. We demonstrate the stability results on a general nonlinear system with switching dynamics and state jumps.

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controllability Metrics, Limitations and Algorithms for Complex Networks

Controllability Metrics, Limitations and Algorithms for Comp...

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American control Conference

作者： Fabio Pasqualetti Sandro Zampieri Francesco Bullo Mechanical Engineering Department University of California at Riverside Department of Information Engineering University of Padova Italy Mechanical Engineering Department and the Center for Control Dynamical Systems and Computation University of California at Santa Barbara

ISBN: (纸本)9781479932757

This paper studies the problem of controlling stable and symmetric complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to drive a network to a target state. We adopt the smallest eigenvalue of the controllability Gramian as metric for the controllability degree of a network, as it identifies the energy needed to accomplish the control task. In the first part of the paper we characterize tradeoffs between the control energy and the number of control nodes, based on the network topology and weights. Our bounds show for instance that, if the number of control nodes is constant, then the control energy increases exponentially with the number of network nodes. Consequently, despite the classic controllability notion, few nodes cannot in practice arbitrarily symmetric control complex networks. In the second part of the paper we propose a distributed open-loop strategy with performance guarantees for the control of complex networks. In our strategy we select control nodes based on network partitioning, and we design the control input based on optimal and distributed control techniques. For our control strategy we show that the control energy depends on the controllability properties of the clusters and on their coupling strength, and it is independent of the network dimension.

关键词： Power control complex networks controllability control node control input Ganglia control task network node Network topology

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Synchronization and power sharing for droop-controlled inverters in islanded microgrids

Synchronization and power sharing for droop-controlled inver...

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作者： Simpson-Porco, John W. Dörfler, Florian Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara CA 93106 United States

Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms, which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it preserves the power sharing properties of the primary droop controller. Our results hold for any acyclic network topology, and hold without assumptions on identical line admittances or voltage magnitudes. © 2013 Elsevier Ltd. All rights reserved.

关键词： Synchronization

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State and parameter estimation of nonlinear systems: a multi-observer approach

State and parameter estimation of nonlinear systems: a multi...

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IEEE Annual Conference on Decision and control

作者： Michelle S. Chong Dragan Nesic Romain Postoyan Levin Kuhlmann Center for Control Dynamical-systems and Computation (CCDC) University of California Santa Barbara CA 93106-9560 USA Department of Electrical and Electronic Engineering the University of Melbourne Australia Universite de Lorraine CRAN UMR 7039 and the CNRS CRAN UMR 7039 France

ISBN: (纸本)9781467360890

We present a multi-observer approach for the parameter and state estimation of continuous-time nonlinear systems. For nominal parameter values in the known parameter set, state observers are designed with a robustness property. At any time instant, one observer is selected by a given criterion to provide its state estimate and its corresponding nominal parameter value. Provided that a persistency of excitation condition holds, we guarantee the convergence of state and parameter estimates up to a given margin of error which can be reduced by increasing the number of observers. The potential computational burden of the scheme is eased by introducing a dynamic parameter re-sampling technique, where the nominal parameter values are iteratively updated using a zoom-in procedure on the parameter set. We illustrate the efficacy of the algorithm on a model of neural dynamics.

关键词： State estimation Parameter estimation Observers

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Real-time Pricing Leading to Optimal Operation under Distributed Decision Makings

Real-time Pricing Leading to Optimal Operation under Distrib...

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American control Conference

作者： Kenji Hirata Joao P. Hespanha Kenko Uchida Department of Mechanical Engineering Nagaoka University of Technology Nagaoka 940 2188 Japan Center for Control Dynamical Systems and Computation and the Department of Electrical and Computer Engineering University of California Santa Barbara CA 93106 USA Department of Electrical Engineering and Bioscience Waseda University Tokyo 169 8555 Japan

ISBN: (纸本)9781479932757

This paper investigates the optimal regulation problem with the steady-state constraints under distributed decision makings, where each agent is allowed to determine its own optimal set-point according to an individual profit. On the other hand, the utility, which corresponds to an individual public commission, tries to realize a socially optimal solution that fulfills steady-state constraints. In order to align the individual decision making of each agent with the socially optimal solution, the utility is allowed to provide additional price, which corresponds to tax or subsidy for the agent. This paper proposes a real-time pricing strategy of the utility. The proposed pricing strategy is heuristic, but we show that the resulting closed-loop system is stable, if the step size parameter in the real-time pricing strategy is sufficiently small, and realizes tracking to the socially optimal solution.

关键词： Pricing Optimization Closed loop systems Real-time systems Steady-state Stability analysis Distributed decision making

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Further Results on Distributed Secondary control in Microgrids

Further Results on Distributed Secondary Control in Microgri...

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IEEE Annual Conference on Decision and control

作者： Hedi Bouattour John W. Simpson-Porco Florian Dorfler Francesco Bullo Center for Control Dynamical Systems and Computation University of California at Santa Barbara

ISBN: (纸本)9781467357159

This work presents several analysis and design results for primary droop control and secondary control in inductive microgrids. Building on our recent work, we study the problem of set point design in droop-controlled microgrids, and provide a choice of droop coefficients leading to the desired power flows. We then compare and contrast two distributed secondary controllers, and extend them to the case where only a fraction of inverters cooperate in regulating the network frequency. We show that both these secondary-control schemes achieve frequency regulation in the presence of resistive losses.

关键词： Inverters Synchronization Stability analysis Microgrids Frequency control Steady-state Vectors

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Novel results on slow coherency in consensus and power networks

Novel results on slow coherency in consensus and power netwo...

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European control Conference (ECC)

作者： Diego Romeres Florian Dörfler Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara

ISBN: (纸本)9781479901890

We revisit the classic slow coherency and area aggregation approach to model reduction in power networks. The slow coherency approach is based on identifying sparsely and densely connected areas of a network, within which all generators swing coherently. A time-scale separation and singular perturbation analysis then results in a reduced low-order system, where coherent areas are collapsed into aggregate variables. Here, we study the application of slow coherency and area aggregation to first-order consensus systems and second-order power system swing dynamics. We unify different theoretic approaches and ideas found throughout the literature, we relax some technical assumptions, and we extend existing results. In particular, we provide a complete analysis of the second-order swing dynamics - without restrictive assumptions on the system damping. Moreover, we identify the reduced aggregate models as generalized first or second-order Laplacian flows with multiple time constants, aggregate damping and inertia matrices, and possibly adverse interactions.

关键词： Aggregates Laplace equations Power system dynamics Symmetric matrices Damping Vectors Generators

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