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Master equations and quantum trajectories for squeezed wave packets

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arXiv 2021年

作者： Gross, Jonathan A. Baragiola, Ben Stace, T.M. Combes, Joshua Center for Quantum Information and Control University of New Mexico AlbuquerqueNM87131-0001 United States Institut Quantique Université de Sherbrooke SherbrookeQCJ1K 2R1 Canada Centre for Quantum Computation & Communication Technology School of Science RMIT University MelbourneVIC3000 Australia ARC Centre for Engineered Quantum System Department of Physics University of Queensland BrisbaneQLD4072 Australia Department of Electrical Computer and Energy Engineering University of Colorado Boulder BoulderCO80309 United States

The interaction between matter and squeezed light has mostly been treated within the approximation that the field correlation time is small. Methods for treating squeezed light with more general correlations currently involve explicitly modeling the systems producing the light. We develop a general purpose input-output theory for a particular form of narrowband squeezed light-a squeezed wave-packet mode-that only cares about the statistics of the squeezed field and the shape of the wave packet. This formalism allows us to derive the input-output relations and the master equation. We also consider detecting the scattered field using photon counting and homodyne measurements which necessitates the derivation of the stochastic master equation. The non Markovian nature of the field manifests itself in the master equation as a coupled hierarchy of equations. We illustrate these with consequences for the decay and resonance fluorescence of two-level atoms in the presence of such fields. Copyright © 2021, The Authors. All rights reserved.

关键词： Wave packets

Reconstructing network structures from partial measurements

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arXiv 2020年

作者： Tyloo, Melvyn Delabays, Robin Jacquod, Philippe Department of Quantum Matter Physics University of Geneva GenevaCH-1211 Switzerland School of Engineering University of Applied Sciences of Western Switzerland HES-SO SionCH-1951 Switzerland Automatic Control Laboratory ETH Zürich ZürichCH-8092 Switzerland Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106-5070 United States

The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is therefore highly desirable, for instance to develop efficient control schemes, to accurately predict the dynamics or to better understand inter-agent processes. In many important and interesting situations, the network structure is not known, however, and previous investigations have shown how it may be inferred from complete measurement time series, on each and every agent. These methods implicitly presuppose that, even though the network is not known, all its nodes are. Here we investigate the different problem of inferring network structures within the observed/measured agents. For symmetrically-coupled dynamical systems close to a stable equilibrium, we establish analytically and illustrate numerically that velocity signal correlators encode not only direct couplings, but also geodesic distances in the coupling network, within the subset of measurable agents. When dynamical data are accessible for all agents, our method is furthermore algorithmically more efficient than the traditional ones, because it does not rely on matrix inversion. Copyright © 2020, The Authors. All rights reserved.

关键词： Dynamical systems

Locating line and node disturbances in networks of diffusively coupled dynamical agents

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arXiv 2020年

作者： Delabays, Robin Pagnier, Laurent Tyloo, Melvyn Automatic Control Laboratory ETH Zurich ZurichCH-8092 Switzerland Center for Control Dynamical Systems and Computation UCSB Santa BarbaraCA93106-5070 United States Department of Mathematics University of Arizona TucsonAZ85721 United States Department of Quantum Matter Physics University of Geneva GenevaCH-1211 Switzerland School of Engineering University of Applied Sciences of Western Switzerland HES-SO SionCH-1951 Switzerland

A wide variety of natural and human-made systems consist of a large set of dynamical units coupled into a complex structure. Breakdown of such systems can have a dramatic impact, as in the case of neurons in the brain or lines in an electric grid, to name but a few. Preventing such catastrophic events requires in particular to be able to detect and locate the source of disturbances as fast as possible. We propose a simple method to identify and locate disturbances in networks of coupled dynamical agents, relying only on time series measurements and on the knowledge of the (possibly Kron-reduced) network structure. The strength and the appeal of the present approach lies in its simplicity paired with the ability to precisely locate disturbances and even to differentiate between line and node disturbances. If we have access to measurement at only a subset of nodes, our method is still able to identify the location of the disturbance if the disturbed nodes are measured. If not, we manage to identify the region of the network where the disturbance occurs. © 2020, CC BY.

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Maximum-matching capture strategies for 3D heterogeneous multiplayer reach-avoid games

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arXiv 2019年

作者： Yan, Rui Duan, Xiaoming Shi, Zongying Zhong, Yisheng Bullo, Francesco Department of Automation Tsinghua University Beijing100084 China Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States

This paper studies a 3D multiplayer reach-avoid game with a goal region and a play region. Multiple pursuers defend the goal region by consecutively capturing multiple evaders in the play region. The players have heterogeneous moving speeds and the pursuers have heterogeneous capture radii. First, we introduce an evasion space (ES) method characterized by a potential function to construct a guaranteed pursuer winning strategy. Then, based on this strategy, we develop conditions to determine whether a pursuit team can guard the goal region against one evader. It is shown that in 3D, if a pursuit team is able to defend the goal region against an evader, then at most three pursuers in the team are necessarily needed. We also compute the value function of the Hamilton-Jacobi-Isaacs (HJI) equation via a convex program and obtain optimal strategies for the players. To capture the maximum number of evaders, we formulate a maximum bipartite matching problem with conflict graph (MBMC). We show that the MBMC is NP-hard and design a polynomial-time constant-factor approximation algorithm to solve it. Finally, we propose a receding horizon strategy for the pursuit team where in each horizon an MBMC is solved and the pursuers adopt the optimal pursuit strategy. We also extend our results to the case of a bounded convex play region where the evaders escape through an exit. Two numerical examples are provided to demonstrate the obtained results. Copyright © 2019, The Authors. All rights reserved.

关键词： Convex optimization

Finite-time influence systems and the wisdom of crowd effect

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arXiv 2019年

作者： Bullo, Francesco Fagnani, Fabio Franci, Barbara Mechanical Engineering Department and the Center of Control Dynamical-Systems and Computation UC Santa BarbaraCA93106-5070 United States Department of Mathematical Sciences Politecnico di Torino Torino Italy

Recent contributions have studied how an inuence system may affect the wisdom of crowd phenomenon. In the so-called naïve learning setting, a crowd of individuals holds opinions that are statistically independent estimates of an unknown parameter;the crowd is wise when the average opinion converges to the true parameter in the limit of infinitely many individuals. Unfortunately, even starting from wise initial opinions, a crowd subject to certain inuence systems may lose its wisdom. It is of great interest to characterize when an inuence system preserves the crowd wisdom effect. In this paper we introduce and characterize numerous wisdom preservation properties of the basic French-DeGroot inuence system model. Instead of requiring complete convergence to consensus as in the previous naïve learning model by Golub and Jackson, we study finite-time executions of the French-DeGroot inuence process and establish in this novel context the notion of prominent families (as a group of individuals with outsize inuence). Surprisingly, finite-time wisdom preservation of the inuence system is strictly distinct from its infinite-time version. We provide a comprehensive treatment of various finite-time wisdom preservation notions, counterexamples to meaningful conjectures, and a complete characterization of equal-neighbor inuence systems. Copyright © 2019, The Authors. All rights reserved.

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A concept of a measuring system for probe kinesthetic parameters identification during echocardiography examination

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arXiv 2020年

作者： Winiarski, Tomasz Balsam, Pawel Węgierek, Maciej Borodzicz-Jażdżyk, Sonia Dudek, Wojciech Banachowicz, Konrad Kochanowski, Janusz Marchel, Michal Warsaw University of Technology Institute of Control and Computation Engineering Nowowiejska 15/19 Warsaw00-665 Poland Department of Cardiology Medical University of Warsaw University Clinical Center Banacha 1a Warsaw02-097 Poland Nomagic Sp. z o.o. ul. Rakowiecka 36 Warsaw02-532 Poland

Echocardiography is the most commonly used imaging technique in clinical cardiology. Due to the high demand for this type of examination and the small number of specialists, there is a need to support the examination process through telemedicine. Moreover, specialist training can be supported by appropriate simulation systems. For (i) creating tailor-made tele-echo robots, (ii) creating echo system simulators, and (iii) conducting echo examination with local or remote expert assistance, knowledge about echo probe kinesthetic parameters during echocardiography examination is advisable. The article describes the concept of a measuring system for obtaining such *** Codes J.3 Copyright © 2020, The Authors. All rights reserved.

关键词： Echocardiography

The scenario approach meets uncertain variational inequalities and game theory

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arXiv 2019年

作者： Paccagnan, Dario Campi, Marco C. Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa Barbara CA93106-5070 United States Dipartimento di Ingegneria dell'Informazione Università di Brescia Italy

Variational inequalities are modelling tools used to capture a variety of decision-making problems arising in mathematical optimization, operations research, game theory. The scenario approach is a set of techniques developed to tackle stochastic optimization problems, take decisions based on historical data, and quantify their risk. The overarching goal of this manuscript is to bridge these two areas of research, and thus broaden the class of problems amenable to be studied under the lens of the scenario approach. First and foremost, we provide out-of-samples feasibility guarantees for the solution of variational and quasi variational inequality problems. Second, we apply these results to two classes of uncertain games. In the first class, the uncertainty enters in the constraint sets, while in the second class the uncertainty enters in the cost functions. Finally, we exemplify the quality and relevance of our bounds through numerical simulations on a demand-response model. Copyright © 2019, The Authors. All rights reserved.

关键词： Variational techniques

Small-signal stability of grid-tied inverter networks

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arXiv 2019年

作者： Jafarpour, Saber Purba, Victor Dhople, Sairaj V. Johnson, Brian Bullo, Francesco Department of Mechanical Engineering Center of Control Dynamical Systems and Computation University of California Santa BarbaraCA93106 United States Department of Electrical and Computer Engineering University of Minnesota MinneapolisMN55414 United States Department of Electrical Engineering University of Washington SeattleWA98195 United States

This paper considers the small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We identify a suitable time-scale decomposition for the inverter dynamics and, using singular perturbation theory, we obtain an analytic sufficient condition for the small-signal stability of the network. In contrast to the alternative of performing an eigenvalue analysis of the full-order network dynamics, our analytic sufficient condition has the benefit of reducing computational complexity and yielding insights on the role of network topology and constitution as well as inverter filter and control parameters on small-signal stability. Our numerical analysis for an inverter network with radial topology validates the approach and illustrates the efficiency of our analytic conditions for designing/monitoring grid-tied inverter networks. Copyright © 2019, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Performance–guaranteed consensus control inspired by the mammalian limbic system for a class of nonlinear multi-agents ⁎

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IFAC-PapersOnLine 2020年第2期53卷 9496-9501页

作者： Ignacio Rubio Scola Luis Rodolfo Garcia Carrillo João P. Hespanha Rogelio Lozano CIFASIS (CONICET-UNR) and Department of Mathematics National University of Rosario Rosario 2000 Argentina. Unmanned Systems Laboratory. School of Engineering and Computer Sciences Texas A&M University - Corpus Christi TexasUSA. 78412-5797. Center for Control Dynamical Systems and ComputationUniversity of California Santa Barbara CA 93106 USA. Heuristique et Diagnostic des Systemes Complexes Universit é de Technologie de Compiègne UMR CNRS 7253 60200 CompiegneFrance

computational models of emotional learning observed in the mammalian brain have inspired diverse self-learning control approaches. These architectures are promising in terms of their fast learning ability and low computational cost. In this paper, the objective is to establish performance–guaranteed emotional learning–inspired control (ELIC) strategies for autonomous multi–agent systems (MAS), where each agent incorporates an ELIC structure to support the consensus controller. The objective of each ELIC structure is to identify and compensate model differences between the theoretical assumptions taken into account when tuning the consensus protocol, and the real conditions encountered in the real system to be stabilized. Stability of the closed-loop MAS is demonstrated using a Lyapunov analysis. Simulation results based on the consensus task of a group of inverted pendulums demonstrate the effectiveness of the proposed ELIC for stabilization of nonlinear MAS.

关键词： Multi-agents systems Biologically-inspired control Robust control Distributed control Nonlinear control