Information and Entropy Flow in the Kalman?Bucy Filter

Mitter, Sanjoy K.; Newton, Nigel J.

doi:10.1007/s10955-004-8781-9

Cited by 86 publications

(86 citation statements)

References 25 publications

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“…Control engineers have also addressed similar topics from the point of view of dynamical systems [54,55] using models and techniques of optimal control theory [1,56] as the Linear-Quadratic-Gaussian control or the Kalman filter. The development of the links between physics, information theory and control theory will allow to quantify and to establish constraints to the increase of performance reachable with a given amount of information in general feedback controlled systems.…”

Section: Discussionmentioning

confidence: 99%

“…Some techniques of filtering theory might be useful for the study of the information and entropy flows associated with continuous-time processes in non-equilibrium statistical mechanical systems [54]. In addition, methods of optimal control theory have been proven useful to compute limits on how much work can be extracted from linear systems [55].…”

Section: Continuous Actuation Of the Feedback Controllermentioning

confidence: 99%

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Open Problems on Information and Feedback Controlled Systems

Cao

Feito

2012

Entropy

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Feedback or closed-loop control allows dynamical systems to increase their performance up to a limit imposed by the second law of thermodynamics. It is expected that within this limit, the system performance increases as the controller uses more information about the system. However, despite the relevant progresses made recently, a general and complete formal development to justify this statement using information theory is still lacking. We present here the state-of-the-art and the main open problems that include aspects of the redundancy of correlated operations of feedback control and the continuous operation of feedback control. Complete answers to these questions are required to firmly establish the thermodynamics of feedback controlled systems. Other relevant open questions concern the implications of the theoretical results for the limitations in the performance of feedback controlled flashing ratchets, and for the operation and performance of nanotechnology devices and biological systems.

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Section: Discussionmentioning

confidence: 99%

Section: Continuous Actuation Of the Feedback Controllermentioning

confidence: 99%

Open Problems on Information and Feedback Controlled Systems

Cao

Feito

2012

Entropy

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“…There are works where entropy maximization is being used in Kalman filtering [12][13][14]. For example, [14] uses entropy maximization as one of the approximation tools to reduce uncertainty.…”

Section: Maximum Relative Entropy and Kalmanmentioning

confidence: 99%

The Kalman Filter Revisited Using Maximum Relative Entropy

Giffin

Urniezius

2014

Entropy

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In 1960, Rudolf E. Kalman created what is known as the Kalman filter, which is a way to estimate unknown variables from noisy measurements. The algorithm follows the logic that if the previous state of the system is known, it could be used as the best guess for the current state. This information is first applied a priori to any measurement by using it in the underlying dynamics of the system. Second, measurements of the unknown variables are taken. These two pieces of information are taken into account to determine the current state of the system. Bayesian inference is specifically designed to accommodate the problem of updating what we think of the world based on partial or uncertain information. In this paper, we present a derivation of the general Bayesian filter, then adapt it for Markov systems. A simple example is shown for pedagogical purposes. We also show that by using the Kalman assumptions or "constraints", we can arrive at the Kalman filter using the method of maximum (relative) entropy (MrE), which goes beyond Bayesian methods. Finally, we derive a generalized, nonlinear filter using MrE, where the original Kalman Filter is a special case. We further show that the variable relationship can be any function, and thus, approximations, such as the extended Kalman filter, the unscented Kalman filter and other Kalman variants are special cases as well.

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“…More recently [13] has sought to formalize classical thermodynamics in the mathematical language of modern dynamical systems (see also [5]). In [27] information flow and entropy have been studied in the context of the Kalman filter. In [31] it is shown that a linear macroscopic dissipative system can be approximated by a linear lossless microscopic system over arbitrary long time intervals.…”

Section: Introductionmentioning

confidence: 99%

Feedback control and the arrow of time

Georgiou

Smith

2010

International Journal of Control

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The purpose of this paper is to highlight the central role that the time asymmetry of stability plays in feedback control. We show that this provides a new perspective on the use of doubly-infinite or semi-infinite time axes for signal spaces in control theory. We then focus on the implication of this time asymmetry in modeling uncertainty, regulation and robust control. We point out that modeling uncertainty and the ease of control depend critically on the direction of time. We also discuss the relationship of this control-based time-arrow with the well known arrows of time in physics.

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Information and Entropy Flow in the Kalman?Bucy Filter

Cited by 86 publications

References 25 publications

Open Problems on Information and Feedback Controlled Systems

Open Problems on Information and Feedback Controlled Systems

The Kalman Filter Revisited Using Maximum Relative Entropy

Feedback control and the arrow of time

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