Feedback control and the arrow of time

Georgiou, Tryphon T.; Smith, Malcolm

doi:10.1080/00207171003682655

Cited by 13 publications

(9 citation statements)

References 42 publications

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“…As stated in Theorem 1 [10], a function g ∈ H2 is cyclic if and only if g/ḡ belong to J , the set of unimodular functions that are quotients of inner functions, 6 i.e., J = {ϕ/ψ : ϕ, ψ inner}. This result is central to our characterization of backward deterministic rank-one processes, and leads to our main result.…”

Section: Rank-one Processesmentioning

confidence: 72%

“…Proof: See the Appendix. 6 The set J is dense in the set of all unimodular functions with respect to L 2 -norm. See [19] for more discussion on J .…”

Section: Rank-one Processesmentioning

confidence: 99%

“…The paradox of the apparent directionality of physics originating in physical laws that are time-symmetric is a key conundrum; Feynman states that there is a fundamental law which says, that "uxels only make wuxels and not vice versa," but we have not found this yet. Thus, the time reversibility of physical models, as well as the lack, are of great interest, see, e.g., [4], [5], [6]. In a similar vain, it is expected that the time-arrow will draw increasingly more attention in modeling of engineering systems as well.…”

Section: Introductionmentioning

confidence: 99%

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The Role of the Time-Arrow in Mean-Square Estimation of Stochastic Processes

Chen

Karlsson

Georgiou

2018

IEEE Control Syst. Lett.

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Abstract-The purpose of this paper is to explain a certain dichotomy between the information that the past and future values of a multivariate stochastic process carry about the present. More specifically, vectorvalued, second-order stochastic processes may be deterministic in one time-direction and not the other. This phenomenon, which is absent in scalar-valued processes, is deeply rooted in the geometry of the shiftoperator. The exposition and the examples we discuss are based on the work of Douglas, Shapiro and Shields on cyclic vectors of the backward shift and relate to classical ideas going back to Wiener and Kolmogorov. We focus on rank-one stochastic processes for which we present a characterization of all regular processes that are deterministic in the reverse time-direction. The paper builds on examples and the goal is to provide pertinent insights to a control engineering audience.

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Section: Rank-one Processesmentioning

confidence: 72%

“…Proof: See the Appendix. 6 The set J is dense in the set of all unimodular functions with respect to L 2 -norm. See [19] for more discussion on J .…”

Section: Rank-one Processesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Role of the Time-Arrow in Mean-Square Estimation of Stochastic Processes

Chen

Karlsson

Georgiou

2018

IEEE Control Syst. Lett.

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“…The discrete-time state-space matrices in (11) are obviously not the same as the continuous-time matrices defined in (1). .…”

Section: Discussionmentioning

confidence: 99%

Model-based control of vortex shedding at low Reynolds numbers

Illingworth

2016

Theor. Comput. Fluid Dyn.

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Model-based feedback control of vortex shedding at low Reynolds numbers is considered. The feedback signal is provided by velocity measurements in the wake, and actuation is achieved using blowing and suction on the cylinder's surface. Using two-dimensional direct numerical simulations and reduced-order modelling techniques, linear models of the wake are formed at Reynolds numbers between 45 and 110. These models are used to design feedback controllers using H ∞ loop-shaping. Complete suppression of shedding is demonstrated up to Re = 110-both for a single-sensor arrangement and for a three-sensor arrangement. The robustness of the feedback controllers is also investigated by applying them over a range of off-design Reynolds numbers, and good robustness properties are seen. It is also observed that it becomes increasingly difficult to achieve acceptable control performance-measured in a suitable way-as Reynolds number increases. which occurred naturally for the oval-shaped cylinder at Reynolds numbers of 77 and above, was suppressed by feedback at Reynolds numbers up to 80.The study of Berger [3] shares a number of features with its earliest successors [8,33,36,42]: all used a velocity measurement in the wake as the feedback signal; in all cases the control law was a simple proportional feedback gain chosen by trial and error (possibly with some phase shift); and all were conducted at low Reynolds numbers near the onset of vortex shedding. (A notable exception is the study by Ffowcs Williams and Zhou [8], performed at a Reynolds number of 400.) The actuation strategies employed in these early studies included transverse displacement of the cylinder [3,42], loudspeakers [8,36] and blowing and suction on the cylinder surface [33].All of these early studies successfully eliminated vortex shedding, but did so only slightly above the critical Reynolds number. Roussopoulos [36], for example, increased the critical Reynolds number by about 20 % in his experimental study, whilst Park et al. [33] increased it by about 27 % in simulations. Gunzburger and Lee [15] achieved complete suppression at slightly higher Reynolds numbers (of Re = 80, about 60 % above criticality) by using surface pressure measurements as the feedback signal and by adding an additional orifice for blowing and suction at the cylinder's trailing edge. Keles [23] used a similar experimental arrangement to Roussopoulos [36] at a higher Reynolds number of 170. The amplitude of vortex shedding was reduced along the entire span of the wake at a streamwise location two cylinder diameters downstream, but it is not clear whether a similar reduction occurred for all streamwise positions. Cohen et al.[7] also used a proportional feedback gain but, rather than use any sensor measurement directly, the controller acted on the first POD mode of a reduced-order model. The amplitude of the POD mode was estimated from several sensor measurements using linear stochastic estimation. Siegel et al. [38] extended this work by applying proportional-differential control to th...

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“…In [31][32][33], the problem of how lossless systems can appear dissipative (compare with [10][11][12] above) is discussed using various perspectives. In [34], how the direction of time affects the difficulty of controlling a process is discussed.…”

Section: Related Workmentioning

confidence: 99%

On Lossless Approximations, the Fluctuation- Dissipation Theorem, and Limitations of Measurements

Delvenne¹,

Doyle²

2011

IEEE Trans. Automat. Contr.

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In this paper, we take a control-theoretic approach to answering some standard questions in statistical mechanics, and use the results to derive limitations of classical measurements. A central problem is the relation between systems which appear macroscopically dissipative but are microscopically lossless. We show that a linear system is dissipative if, and only if, it can be approximated by a linear lossless system over arbitrarily long time intervals. Hence lossless systems are in this sense dense in dissipative systems. A linear active system can be approximated by a nonlinear lossless system that is charged with initial energy. As a by-product, we obtain mechanisms explaining the Onsager relations from time-reversible lossless approximations, and the fluctuation-dissipation theorem from uncertainty in the initial state of the lossless system. The results are applied to measurement devices and are used to quantify limits on the so-called observer effect, also called back action, which is the impact the measurement device has on the observed system. In particular, it is shown that deterministic back * H. Sandberg is with the School of Electrical Engineering, Royal Institute of Technology (KTH), Stockholm, Sweden, hsan@ee.kth.se.

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Feedback control and the arrow of time

Cited by 13 publications

References 42 publications

The Role of the Time-Arrow in Mean-Square Estimation of Stochastic Processes

The Role of the Time-Arrow in Mean-Square Estimation of Stochastic Processes

Model-based control of vortex shedding at low Reynolds numbers

On Lossless Approximations, the Fluctuation- Dissipation Theorem, and Limitations of Measurements

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