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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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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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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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From forced to natural competition in a biologically plausible neural network

From forced to natural competition in a biologically plausib...

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9th Workshop on Self-Organizing Maps, WSOM 2012

作者： Peláez, Francisco Javier Ropero Godoi, Antonio Carlos Center of Mathematics Computation and Cognition Universidade Federal Do ABC Santo André Brazil Department of Telecommunications and Control Engineering Universidade de São Paulo Sao Paulo Brazil

ISBN: (纸本)9783642352294

In this paper we propose a new unsupervised neural network whose units exhibit intrinsic plasticity and metaplasticity. We describe three versions of the network: The first version is a two-layered neural network with intrinsic plasticity governing the shifting of the activation function, and the pre-synaptic rule altering synaptic weights. In this first version, competition is forced, so that the most activated neuron is set to one and the others to zero. In the second version, competition is not forced and occurs naturally due to inhibition between second layer's neurons. Competition also occurs naturally in the third version whose architecture resembles the one of the internal granular layer of the koniocortex. All versions of our network categorize input patterns similarly to a conventional competitive neural network. © 2013 Springer-Verlag.

关键词： Network layers

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Voltage Stabilization in Microgrids via Quadratic Droop control

Voltage Stabilization in Microgrids via Quadratic Droop Cont...

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IEEE Annual Conference on Decision and control

作者： John W. Simpson-Porco Florian Dorfler Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara Department of Electrical Engineering University of California Los Angeles

ISBN: (纸本)9781467357159

Motivated by the growing interest in energy technology and smart grid architectures, we consider the problem of voltage stability and reactive power balancing in low-voltage electrical networks equipped with DC/AC inverters ("microgrids"). It is generally believed that high-voltage equilibria of such networks are stable, but the locations of these equilibria are unknown, as is the critical network load where stability is lost. Inspired by the "control by interconnection" paradigm developed for port-Hamiltonian systems, we propose a novel droop-like inverter controller which is quadratic in the local voltage magnitude. Remarkably, under this controller the closed-loop network is again a well-posed electrical circuit. We find that the equilibria of the quadratic droop-controlled network are in exact correspondence with the solutions of a reduced power flow equation. For general network topologies, we study some simple yet insightful solutions of this equation, and for the frequently-encountered case of a parallel microgrid, we present a concise and closed-form condition for the existence of an exponentially stable high-voltage network equilibrium. Our condition establishes the existence of a critical inductive load for the network, which depends only on the network topology, admittances, and controller gains. We compare and contrast our design with the conventional droop controller, investigate the relationship between the two, and validate the robustness of our design through simulation.

关键词： Inverters Microgrids Equations Voltage control Mathematical model Vectors Reactive power

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Direct Numerical Solution of Algebraic Lyapunov Equations For Large-Scale Systems Using Quantized Tensor Trains

Direct Numerical Solution of Algebraic Lyapunov Equations Fo...

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IEEE Annual Conference on Decision and control

作者： Michael Nip Joao P. Hespanha Mustafa Khammash Center for Control Dynamical Systems and Computation University of California Santa Barbara California USA 93106 Center for Control Dynamical Systems and Computation University of California Santa Barbara California USA 93106 Department of Biosystems Science and Engineering ETH-Zurich 4058 Basel Switzerland

ISBN: (纸本)9781467357159

We present a novel method for solving high-dimensional algebraic Lyapunov equations exploiting the recently proposed Quantized Tensor Train (QTT) numerical linear algebra. A key feature of the approach is that given a prescribed error tolerance, it automatically calculates the optimal lowest rank approximation of the solution in the Frobenius norm. The low rank nature of the approximation potentially enables a sublinear scaling of the computational complexity with the number of states of the dynamical system. The resulting solutions appear in a new matrix tensor format which we call the Vectorized-QTT-Matrix format. We show the effectiveness of our method by calculating the controllability Gramians for discretized reaction-diffusion equations. We introduce an algorithm for the new tensor format of the solution for calculating the matrix-by-vector product and combine it with the celebrated Lanczos algorithm to compute the dominant eigenvalues/eigenvectors of the matrix.

关键词： large-scale systems Tensor TRAIN Algebra NUMERICAL SOLUTION

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Randomized sampling for large zero-sum games

Randomized sampling for large zero-sum games

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作者： Bopardikar, Shaunak D. Borri, Alessandro Hespanha, João P. Prandini, Maria Di Benedetto, Maria D. United Technologies Research Center Inc. Berkeley CA United States Rome Italy Center for Control Dynamical Systems and Computation University of California Santa Barbara CA 93106 United States Dipartimento di Elettronica Informazione e Bioingegneria Politecnico di Milano Italy Department of Electrical and Information Engineering University of l'Aquila Italy

This paper addresses the solution of large zero-sum matrix games using randomized methods. We formalize a procedure, termed as the sampled security policy (SSP) algorithm, by which a player can compute policies that, with a high confidence, are security policies against an adversary using randomized methods to explore the possible outcomes of the game. The SSP algorithm essentially consists of solving a stochastically sampled subgame that is much smaller than the original game. We also propose a randomized algorithm, termed as the sampled security value (SSV) algorithm, which computes a high-confidence security-level (i.e., worst-case outcome) for a given policy, which may or may not have been obtained using the SSP algorithm. For both the SSP and the SSV algorithms we provide results to determine how many samples are needed to guarantee a desired level of confidence. We start by providing results when the two players sample policies with the same distribution and subsequently extend these results to the case of mismatched distributions. We demonstrate the usefulness of these results in a hide-and-seek game that exhibits exponential complexity. © 2013 Elsevier Ltd. All rights reserved.

关键词： Game theory

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Finite-Field Consensus

Finite-Field Consensus

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IEEE Annual Conference on Decision and control

作者： Fabio Pasqualetti Domenica Borra Francesco Bullo Mechanical Engineering Department University of California Riverside Dipartimento di Scienze Matematiche Politecnico di Torino Italy Center for Control Dynamical Systems and Computation University of California at Santa Barbara

ISBN: (纸本)9781467357159

This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers {0,...,p - 1}, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions on the network topology and weights to ensure convergence. For instance we show that, differently from the case of consensus networks over the field of real numbers, consensus networks over finite fields converge in finite time, and that properties of the agents interaction graph are not sufficient to ensure finite-field consensus. Finally, we discuss the application of finite-field consensus to distributed averaging in sensor networks.

关键词： Galois fields Network topology Prime number Converge Sufficient conditions

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Sparse and Optimal Wide-Area Damping control in Power Networks

Sparse and Optimal Wide-Area Damping Control in Power Networ...

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American control Conference

作者： Florian Dorfler Mihailo R. Jovanovic Michael Chertkov Francesco Bullo Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106 Department of Electrical and Computer Engineering University of Minnesota Minneapolis MN 55455 Theory Division & Center for Nonlinear Studies at LANL and with New Mexico Consortium Los Alamos NM 87544

ISBN: (纸本)9781479901777

Inter-area oscillations in power networks are typically poorly controllable by means of local decentralized control. Recent research efforts have been aimed at developing wide-area control strategies that involve communication of remote signals. In conventional wide-area control strategies the control structure is fixed a priori typically based on modal criteria. In contrast, here we employ the recently introduced paradigm of sparsity-promoting optimal control to simultaneously identify the control structure and optimize the closed-loop performance. To induce a sparse control architecture, we regularize the standard quadratic performance index with an l_1-penalty on the feedback matrix. The quadratic objective functions are inspired by the classic slow coherency theory and are aimed at imitating homogeneous networks without interarea oscillations. We use a compelling example to demonstrate that the proposed combination of the sparsity-promoting optimal control design with the slow coherency objective functions performs almost as well as the optimal centralized controllers.

关键词： Power grids control Architecture damped control design control Objective function Optimal control quadratic performance index homogeneous network

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Distributed estimation via iterative projections with application to power network monitoring

Distributed estimation via iterative projections with applic...

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作者： Pasqualetti, Fabio Carli, Ruggero Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara United States Department of Information Engineering University of Padova Padova Italy

This work presents a distributed method for control centers to monitor the operating condition of a power network, i.e.;to estimate the network state, and to ultimately determine the occurrence of threatening situations. State estimation has been recognized to be a fundamental task for network control centers to operate safely and reliably a power grid. We consider (static) state estimation problems, in which the state vector consists of the voltage magnitude and angle at all network buses. We consider the state to be linearly related to network measurements, which include power flows, current injections, and voltage phasors at some buses. We admit the presence of several cooperating control centers, and we design two distributed methods for them to compute the minimum variance estimate of the state, given the network measurements. The two distributed methods rely on different modes of cooperation among control centers: in the first method an incremental mode of cooperation is used, whereas, in the second method, a diffusive interaction is implemented. Our procedures, which require each control center to know only the measurements and the structure of a subpart of the whole network, are computationally efficient and scalable with respect to the network dimension, provided that the number of control centers also increases with the network cardinality. Additionally, a finite-memory approximation of our diffusive algorithm is proposed, and its accuracy is characterized. Finally, our estimation methods are exploited to develop a distributed algorithm to detect corrupted network measurements. © 2012 Elsevier Ltd. All rights reserved.

关键词： State estimation

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