Feedback Control Under Data Rate Constraints: An Overview

Nair, Girish N.; Fagnani, Fabio; Zampieri, Sandro; Evans, R.J.

doi:10.1109/jproc.2006.887294

Cited by 906 publications

(646 citation statements)

References 69 publications

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“…For a linear time invariant (LTI) plant it is well understood that its unstable poles, non minimum phase (NMP) zeros and time-delay will cause unavoidable limitations in performance (see for example Seron et al (1997) and references therein). In more recent years, the study of fundamental limitations has been extended to problems of control over communication channels and has attracted growing interest (see for example Antsaklis and Baillieul (2004) and the recent survey by Nair et al (2007)). …”

Section: Introductionmentioning

confidence: 99%

“…It follows from Braslavsky et al (2005) that for a system with one unstable pole the increase in SNR is exponential in the magnitude of the time-delay and that of the unstable pole. A consistent deterioration in control performance imposed by time-delays has been characterised in Nair et al (2007) in a (discrete-time) data-rate constrained control framework. The present paper extends the continuous-time results by Braslavsky et al (2007) to systems with time-delay and feedback over bandwidth-limited additive coloured Gaussian noise (ACGN) channels.…”

Section: Introductionmentioning

confidence: 99%

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Fundamental limitations in control over a communication channel

Rojas¹,

Braslavsky²,

Middleton

2008

Automatica

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Fundamental limitations in feedback control is a well established area of research. In recent years it has been extended to the study of limitations imposed by the consideration of a communication channel in the control loop. Previous results characterised these limitations in terms of a minimal data transmission rate necessary for stabilisation. In this paper a signal-to-noise ratio (SNR) approach is used to obtain a tight condition for the linear time invariant output feedback stabilisation of a continuous-time, unstable, non minimum phase (NMP) plant with time-delay over an additive Gaussian coloured noise communication channel. By working on a linear setting the infimal SNR for stabilisability is defined as the infimal achievable H 2 norm between the channel noise input and the channel signal input. The result gives a guideline in estimating the severity of the fundamental SNR limitation imposed by the plant unstable poles, NMP zeros, time-delay as well as the channel NMP zeros, bandwidth, and channel noise colouring.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fundamental limitations in control over a communication channel

Rojas¹,

Braslavsky²,

Middleton

2008

Automatica

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“…This implies that gene expression is inherently unstable in the formal control theory sense of the data rate theorem (Nair et al 2007) and must be stabilized by provision of control information at a critical rate. Failure to provide control information at or above that rate initiates characteristic modes of system failure that, for neural systems, are expressed as developmental disorders.…”

Section: A Control Theory Modelmentioning

confidence: 99%

“…1 for a schematic. The data rate theorem (Nair et al 2007) states that, for an inherently unstable system, the control information represented by the vector u t must be provided at a rate H that is greater than the rate at which the system produces 'topological information.' For the system of Eq.…”

Section: A Control Theory Modelmentioning

confidence: 99%

Environmental Induction of Neurodevelopmental Disorders

Wallace

2016

Bull Math Biol

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Chemical exposures, pre-and neonatal infections, psychosocial stress, and the cross-generational cultural and epigenetic impacts of these and other toxicants become an integrated, sometimes synergistic, signal that can overwhelm essential neurodevelopmental regulation. We characterize that dynamic through statistical models based on the asymptotic limit theorems of control and information theories. Schizophrenia and autism emerge as two different 'phases' of pathological neurodevelopmental 'condensations' that impair the dynamic, shifting global workspace of normal mental function.

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“…The data-rate theorem, a generalization of the classic Bode integral theorem for linear control systems (e.g., Yu and Mehta, 2010;Kitano, 2007;Csete and Doyle, 2002), describes the stability of linear feedback control under data rate constraints (e.g., Mitter, 2001;Tatikonda and Mitter, 2004;Sahai, 2004;Sahai and Mitter, 2006;Minero et al, 2009;Nair et al, 2007;You and Xie, 2013). Given a noise-free data link between a discrete linear plant and its controller, unstable modes can be stabilized only if the feedback data rate H is greater than the rate of 'topological information' generated by the unstable system.…”

Section: Introductionmentioning

confidence: 99%

Body mass control and unresolved sociocultural stress: application of the generalized Data-Rate Theorem

Wallace

2013

Preprint

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New results from control theory allow construction of necessary conditions statistical models of body mass regulation in the context of interaction with a complex dynamic environment. Focusing on the stressrelated induction of central obesity via failure of HPA axis regulation, we explore implications for strategies of prevention and treatment. It rapidly becomes evident that individual-centered biomedical reductionism is an inadequate paradigm. Absent mitigation of HPA axis or related dysfunctions arising from social pathologies of power imbalance, economic insecurity, and so on, it is unlikely that permanent changes in visceral obesity can be maintained without constant therapeutic effort, an expensive -and likely unsustainable -public policy.

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Feedback Control Under Data Rate Constraints: An Overview

Cited by 906 publications

References 69 publications

Fundamental limitations in control over a communication channel

Fundamental limitations in control over a communication channel

Environmental Induction of Neurodevelopmental Disorders

Body mass control and unresolved sociocultural stress: application of the generalized Data-Rate Theorem

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