Topological feedback entropy for nonlinear stabilization

Nair, Girish N.; Evans, Robin J.; Mareels, Iven; Moran, William

doi:10.1016/s1474-6670(17)31357-5

Cited by 93 publications

(191 citation statements)

References 18 publications

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“…1. Similar block diagram that are concerned with communication imperfections only from system to remote controller has been considered in many research papers, such as [6], [8]- [13]. This block diagram can correspond to the smart oil drilling system that uses down hole telemetry [2] and also tele-operation systems of micro autonomous vehicles [1].…”

Section: B Paper Contributionsmentioning

confidence: 99%

Reference Tracking of Nonlinear Dynamic Systems over AWGN Channel Using Describing Function

Parsa

Farhadi

2018

Scientia Iranica

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This paper presents a new technique for mean square asymptotic reference tracking of nonlinear dynamic systems over Additive White Gaussian Noise (AWGN) channel. The nonlinear dynamic system has periodic outputs to sinusoidal inputs and is cascaded with a bandpass filter acting as encoder.Using the describing function method, the nonlinear dynamic system is represented by an equivalent linear dynamic system. Then, for this system, a mean square asymptotic reference tracking technique including an encoder, decoder and a controller is presented. It is shown that the proposed reference tracking technique results in mean square asymptotic reference tracking of nonlinear dynamic systems over AWGN channel. The satisfactory performance of the proposed reference tracking technique is illustrated using practical example simulations.

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Section: B Paper Contributionsmentioning

confidence: 99%

Reference Tracking of Nonlinear Dynamic Systems over AWGN Channel Using Describing Function

Parsa

Farhadi

2018

Scientia Iranica

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“…Their approach in turn has been motivated by the work of Nair et al [8] on feedback entropies for nonlinear discrete-time systems. The entropy notion considered here may be regarded as a lower bound for the minimum data rate (take the logarithm with base 2 instead of the natural logarithm used, for convenience, in the present paper.)…”

Section: September 15 2009mentioning

confidence: 99%

Entropy of controlled invariant subspaces

Colonius

Helmke

2014

Z Angew Math Mech

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Abstract. For continuous-time linear control systems, a concept of entropy for controlled and almost controlled invariant subspaces is introduced. Upper bounds for the entropy in terms of the eigenvalues of the autonomous subsystem are derived. September 15, 2009Key words. invariance entropy, topological entropy, geometric control, almost (A,B)-invariant subspaces, eigenvalue bounds.AMS subject classifications. 94A17, 37B40, 93C151. Introduction. Controlled and conditioned invariant subspaces of linear dynamical systems play a crucial role in understanding controller design problems such as disturbance decoupling, filtering, robust observer design, and high gain state feedback. In fact, starting form the early work of Basile-Morro [1] and Wonham [14], controlled invariant subspaces became a cornerstone of geometric control theory. In this paper, we begin an investigation of how geometric control design via controlled invariant subspaces is affected by entropy estimates and associated data rate constraints. The main motivation for this circle of ideas comes from the increasing needs of controlling systems with communication constraints, i.e. for systems where the state passes through a communication channel and may thus not be fully available to the controller.As a starting point for such an investigation, we associate to any almost (A, B)-invariant subspace V of a linear control system a number, called the invariance entropy of V, that measures how difficult it is, using open loop controls, to keep the system in V . It is defined by the exponential growth rate of the number of controls necessary to keep the system in an arbitrarily small ε-neighborhood of V . More generally, by extending the familiar notion of topological entropy for the flow defined by A, we define the entropy of an arbitary linear subspace V of the state space. We show that the invariance entropy is finite for any almost (A, B)-invariant subspace and derive upper bounds in terms of the sum of the eigenvalues of A with positive real part. Sharper upper bounds are derived for specific classes of linear systems.Our approach partially extends and follows that by Colonius and Kawan [4], where an entropy-like notion was proposed for controlled invariance of compact subsets of the state space of general control systems. Their approach in turn has been motivated by the work of Nair et al. [8] on feedback entropies for nonlinear discrete-time systems. The entropy notion considered here may be regarded as a lower bound for the minimum data rate (take the logarithm with base 2 instead of the natural logarithm used, for convenience, in the present paper.) More explicit relations to data rates are given in Kawan's PhD thesis [9].

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“…Semi-conjugacy property (10) implies that π out (Q) is controlled invariant. In fact: Let y 2 ∈ π out (Q).…”

Section: Remarkmentioning

confidence: 99%

Invariance entropy for outputs

Colonius

Kawan

2011

Math. Control Signals Syst.

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For continuous-time control systems with outputs, this paper analyzes invariance entropy as a measure for the information rate necessary to achieve invariance of compact subsets of the output space. For linear control systems with compact control range, relations to controllability and observability properties are studied. Furthermore, the notion of asymptotic invariance entropy is introduced and characterized for these systems.

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Topological feedback entropy for nonlinear stabilization

Cited by 93 publications

References 18 publications

Reference Tracking of Nonlinear Dynamic Systems over AWGN Channel Using Describing Function

Reference Tracking of Nonlinear Dynamic Systems over AWGN Channel Using Describing Function

Entropy of controlled invariant subspaces

Invariance entropy for outputs

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