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An online integral reinforcement learning algorithm to solve N-player Nash games

An online integral reinforcement learning algorithm to solve...

引用

IEEE International Symposium on Intelligent control (ISIC)

作者： Kyriakos G. Vamvoudakis Frank L. Lewis Center for Control Dynamical-systems and Computation (CCDC) University of California Santa Barbara CA USA Automation and Robotics Research Institute University of Texas Arlington Fort Worth TX USA

In this paper we introduce an online algorithm that uses integral reinforcement knowledge for learning the continuous-time Nash game (zero-sum and non-zero-sum) solution for nonlinear systems with infinite horizon costs and partial knowledge of the system dynamics. This algorithm is a data based approach to the solution of the coupled Hamilton-Jacobi equations and it does not require explicit knowledge on the system's drift dynamics. A novel adaptive control algorithm is given that is based on policy iteration and implemented using an actor/critic structure for every player in the game having 2N adaptive approximator structures. All 2N approximation networks are adapted simultaneously. Novel adaptive control tuning algorithms are given for the critic and actor networks. The convergence to the Nash solution of the game is proven, and stability of the system is also guaranteed. Simulation examples support the theoretical result.

关键词： Games Equations Heuristic algorithms Tuning Mathematical model Approximation algorithms Artificial neural networks

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Distributed detection of cyber-physical attacks in power networks: A waveform relaxation approach

Distributed detection of cyber-physical attacks in power net...

引用

2011 49th Annual Allerton Conference on Communication, control, and Computing, Allerton 2011

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

ISBN: (纸本)9781457718168

Future power grids will be required to operate safely and reliably against cyber-physical attacks. The large dimensionality and the difficulty in calibrating dynamical network models precludes the use of centralized attack detection algorithms. This paper proposes a unified modeling framework and an advanced detection procedure whose implementation requires only local network knowledge. We model a power network as a linear time-invariant descriptor system and cyber-physical attacks as unknown inputs. This modeling framework captures, for instance, network components malfunction and measurements corruption. In our detection method the power network is partitioned among geographically deployed control centers, possibly located at transmission substations. Each control center has knowledge of only its respective subarea dynamics, is able to acquire information from neighboring areas, and is capable of performing basic computations. Under these minimal technological requirements and a reasonable observability assumption, we design an entirely distributed detection filter which requires only local network knowledge and yet achieves guaranteed global performance. Our detection filter is based on a sparse residual filter in descriptor form, which can be stabilized via decentralized output injection and implemented distributively via waveform relaxation. © 2011 IEEE.

关键词： Electric power transmission networks

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On opinion dynamics in heterogeneous networks

On opinion dynamics in heterogeneous networks

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

ISBN: (纸本)9781457700804

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. © 2011 AACC American Automatic control Council.

关键词： Topology

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On the critical coupling strength for Kuramoto oscillators

On the critical coupling strength for Kuramoto oscillators

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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)9781457700804

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. © 2011 AACC American Automatic control Council.

关键词： Synchronization

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Stochastic strategies for survival: Bacterial competence in Bacillus subtilis

Stochastic strategies for survival: Bacterial competence in ...

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作者： Dandach, Sandra H. Khammash, Mustafa Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106 United States

ISBN: (纸本)9781457700804

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. © 2011 AACC American Automatic control Council.

关键词： DNA

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Algorithms for the traveling salesman problem with neighborhoods involving a Dubins vehicle

Algorithms for the traveling salesman problem with neighborh...

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作者： Isaacs, Jason T. Klein, Daniel J. Hespanha, João P. Center for Control Dynamical Systems and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA 93106 United States

ISBN: (纸本)9781457700804

We study the problem of finding the minimum-length curvature constrained closed path through a set of regions in the plane. This problem is referred to as the Dubins Traveling Salesperson Problem with Neighborhoods (DTSPN). Two algorithms are presented that transform this infinite dimensional combinatorial optimization problem into a finite dimensional asymmetric TSP by sampling and applying the appropriate transformations, thus allowing the use of existing approximation algorithms. We show for the case of disjoint regions, the first algorithm needs only to sample each region once to produce a tour within a factor of the length of the optimal tour that is independent of the number of regions. We present a second algorithm that performs no worse than the best existing algorithm and can perform significantly better when the regions overlap. © 2011 AACC American Automatic control Council.

关键词： Traveling salesman problem

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Hide-and-seek with directional sensing

Hide-and-seek with directional sensing

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

ISBN: (纸本)9783902661937

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 randomdirection, corresponding to a half-plane in which the hidden object is *** 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. © 2011 IFAC.

关键词： Mobile agents

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Cyber-Physical Attacks in Power Networks: Models, Fundamental Limitations and Monitor Design

Cyber-Physical Attacks in Power Networks: Models, Fundamenta...

引用

IEEE Conference on Decision and control

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

ISBN: (纸本)9781612848006

Future power networks will be characterized by safe and reliable functionality against physical and cyber attacks. This paper proposes a unified framework and advanced monitoring procedures to detect and identify network components malfunction or measurements corruption caused by an omniscient adversary. We model a power system under cyber-physical attack as a linear time-invariant descriptor system with unknown inputs. Our attack model generalizes the prototypical stealth, (dynamic) false-data injection and replay attacks. We characterize the fundamental limitations of both static and dynamic procedures for attack detection and identification. Additionally, we design provably-correct (dynamic) detection and identification procedures based on tools from geometric control theory. Finally, we illustrate the effectiveness of our method through a comparison with existing (static) detection algorithms, and through a numerical study.

关键词： Power grids Detection algorithms Detection and identification control Theory power systems

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Distributed detection of cyber-physical attacks in power networks: A waveform relaxation approach

Distributed detection of cyber-physical attacks in power net...

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Annual Allerton Conference on Communication, control, and Computing

作者： Florian Dörfler Fabio Pasqualetti Francesco Bullo Center of Control Dynamical Systems and Computation University of California at Santa Barbara USA

关键词： Mathematical model Equations Power system dynamics Generators Relaxation methods Security Estimation

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A graph-theoretical characterization of power network vulnerabilities

A graph-theoretical characterization of power network vulner...

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

ISBN: (纸本)9781457700804

This work is concerned with the security of a power network against components failure and external attacks. We model a power plant as a linear continuous-time descriptor system. We adopt the framework of structural control theory, and we associate a digraph with the power plant. We provide a necessary and sufficient graph theoretic condition for the existence of vulnerabilities that are inherent to the power network interconnection structure. From a system theoretic perspective, we generalize a known result on the structural rank of the transfer matrix of a state space system to take into account a set of algebraic constraints. © 2011 AACC American Automatic control Council.

关键词： Transfer matrix method

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