Performance analysis and controller improvement for linear systems with (m, k)-firm data losses

Horssen, E.P. van; Behrouzian, Amir; Goswami, Dip; Antunes, Duarte J.; Basten, Twan; Heemels, W.P.M.H.

doi:10.1109/ecc.2016.7810677

Cited by 27 publications

(21 citation statements)

References 14 publications

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“…. θ s ( ) is also given by the eigenvalue of    = + : s s with the largest real part [6] (which can be shown to be real [28]). Derivatives of this dynamical free energy with respect to s can be used to obtain the activity (net count rate)…”

Section: K K Kmentioning

confidence: 99%

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

et al. 2015

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We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-1/2 particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smooth out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.Understanding and controlling the dynamical behavior of quantum systems has seen flourishing interest [1][2][3] propelled by theoretical and experimental progress that has made it possible to observe and manipulate such systems with unprecedented accuracy. Much attention has also been devoted recently to the notion of dynamical phase transitions in such systems, relating them to the nonanalyticity of, e.g., the Loschmidt echo [4] or the logarithm of a biased partition function in large-deviation (LD) theory [5], which has a natural interpretation in terms of the statistics of rare trajectories observed in experiments. The study of the dynamics of quantum systems through LD methods [6-8] emerged recently both as an extension of the theory as applied to classical systems [9][10][11][12] and as a dynamical complement to the standard analysis of equilibrium phase transitions in many-body systems [13]. Here, nonanalyticities in the LD free-energy function of a system, extracted from the equations governing its dynamical behavior, are identified in the literature with dynamical phase transition points [6].Following [6], in this paper we are interested in studying the statistical properties of rare quantum-jump trajectories [14] of a system that interacts with a heat bath driving the system out of equilibrium. We consider the dynamical LD properties of a simple three-spin quantum open model, which departs from those recently studied in two respects: first, dissipation is due to nonclassical bilinear jump operators; and second, we consider a current-like dynamical order parameter. The two central results in this paper are (a) the observation of intermittency between dynamical phases of distinct activity, itself a consequence of the reducibility of the dynamics in an appropriate limit due to the collective jump operators; and (b) the existence of a Gallavotti-Cohen symmetry in LD functions associated with the time-asymmetric order parameter, analogous to that found in driven classical systems [15], which gives rise to a fluctuation theorem [16] relating to the quantum jump rate. Our system therefore provides a minimal but extendible model that uncovers the effects of thermal baths and the nontrivial interplay between local and global decay channels [17] on the non-equilibrium dynamics of a quantum system.We start with three spins-1/2, which we label = j 1, 2, 3, placed at ...

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Section: K K Kmentioning

confidence: 99%

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

et al. 2015

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“…Interest in such systems has grown with recent experimental progress in quantum optics and open quantum many-body systems [6][7][8][9], in particular from the point of view of dynamical phase transitions [10][11][12][13][14][15][16][17][18][19] and system identification [20,21]. [12], and through the thermodynamics of jump trajectories [22][23][24][25]; the large deviations approach to quantum phase transitions exploits both these features to uncover dynamical phases [17,26].…”

Section: Introductionmentioning

confidence: 99%

Sanov and central limit theorems for output statistics of quantum Markov chains

Horssen

Guţǎ

2015

Journal of Mathematical Physics

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Horssen, Merlijn van and Guţă, Mădălin (2015) A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not. C 2015 AIP Publishing LLC. [http://dx Sanov and central limit theorems for output statistics of quantum Markov chains

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“…Such constraints on the data loss signal are often encountered in practice, and arise from the characteristics of the shared (wireless) communication network and/or the embedded architecture. Another type of constraints could be that for every m consecutive time steps, we receive data in good order on at least k time steps (so-called (m, k)-firmness), where m, k ∈ N are given parameters [9], [11], [29].…”

Section: Problem Formulationmentioning

confidence: 99%

“…Now let us modify the constraint on the data loss signal. Consider the case where the control and communication system is constructed so as to protect itself against disruptions, for example, such that at most one packet can be lost in a period of m consecutive steps (or stated otherwise, at least m − 1 successful transmissions take place in every m steps, which is (m, m − 1)-firmness [29]. It turns out that in this case the system is observable (as soon as m ≥ 2).…”

Section: Numerical Examplementioning

confidence: 99%

Observability and Controllability Analysis of Linear Systems Subject to Data Losses

Jungers

Kundu

Heemels

2018

IEEE Trans. Automat. Contr.

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We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete-time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject to disruptions (data losses) in the feedback loop, where the set of possible data loss sequences is captured by an automaton. As such, the results are applicable in the context of shared (wireless) communication networks and/or embedded architectures where some information on the data loss behaviour is available a priori.We propose an algorithm for deciding observability (or the absence of it) for such systems, and show how this algorithm can be used also to decide other properties including constructibility, controllability, reachability, null-controllability, detectability and stabilizability by means of relations that we establish among these properties. The main apparatus for our analysis is the celebrated Skolem's Theorem from linear algebra.Moreover, we study the relation between the model adopted in this paper and a previously introduced model where, instead of allowing dropouts in the feedback loop, one allows for time-varying delays. Index Terms

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Performance analysis and controller improvement for linear systems with (m, k)-firm data losses

Cited by 27 publications

References 14 publications

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

Sanov and central limit theorems for output statistics of quantum Markov chains

Observability and Controllability Analysis of Linear Systems Subject to Data Losses

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