Control Under Communication Constraints

Tatikonda, Sekhar; Mitter, Sanjoy K.

doi:10.1109/tac.2004.831187

Cited by 1,343 publications

(971 citation statements)

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“…The results were obtained in terms of the mutual information rate between the feedback and the reference signals, as well as the channel capacity and the unstable eigenvalues of the LTI system. The lower bound for the channel capacity obtained was expected since it corresponds to the one obtained in previous literature as [12] and [7]. We also obtained a lower bound in terms of the entropy of the reference signal for the maximum achievable accuracy in a tracking system, in the absence of constraint channel.…”

Section: Discussionsupporting

confidence: 77%

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Conditions for tracking in networked control systems

López

Abdallah

Jayaweera

et al. 2008

2008 47th IEEE Conference on Decision and Control

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Abstract-In this paper we obtain information theoretical conditions for tracking in linear time-invariant control systems. We consider the particular case where the closed loop contains a channel in the feedback loop. The mutual information rate between the feedback signal and the reference input signal is used to quantify information about the reference signal that is available for feedback. This mutual information rate must be maximized in order to improve the tracking performance. The mutual information is shown to be upper bounded by a quantity that depends on the unstable eigenvalues of the plant and on the channel capacity. If the channel capacity reaches a lower limit, the feedback signal becomes completely uncorrelated with the reference signal, rendering feedback useless. We also find a lower bound on the expected squared tracking error in terms of the entropy of a random reference signal. Examples and simulations are provided to demonstrate the results.

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Section: Discussionsupporting

confidence: 77%

“…** The research of this author is partially supported by NSF award CNS 0626380 under the FIND initiative. feedback signal is transmitted by means of a finite capacity channel, the mutual information rate is upper bounded by C f − ∑ i=1 max {0, log 2 (|λ i (A)|)}, [12].…”

Section: Introductionmentioning

confidence: 99%

Conditions for tracking in networked control systems

López

Abdallah

Jayaweera

et al. 2008

2008 47th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…Most recently, the attention to quantization has been stimulated by the growing number of application involving "networked" control systems, which are systems interconnected through channels of limited capacity (see e.g. [28], [2]). …”

Section: Dubbini@maildmunipiitmentioning

confidence: 99%

Left invertibility of discrete systems with finite inputs and quantized output

Dubbini

Piccoli

Bicchi

2008

2008 47th IEEE Conference on Decision and Control

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Abstract-The aim of this paper is to address left invertibility for dynamical systems with inputs and outputs in discrete sets. We study systems that evolve in discrete time within a continuous state-space. Quantized outputs are generated by the system according to a given partition of the state-space, while inputs are arbitrary sequences of symbols in a finite alphabet, which are associated to specific actions on the system. We restrict to the case of contractive dynamics for fixed inputs. The problem of left invertibility, i.e. recovering an unknown input sequence from the knowledge of the corresponding output string, is addressed using the theory of Iterated Function Systems (IFS), a tool developed for the study of fractals. We show how the IFS naturally associated to a system and the geometric properties of its attractor are linked to the left invertibility property of the system. Our main results are a necessary and sufficient condition for a given system to be left invertible with probability one on the space of inputs (i.e. for almost all input sequences), and necessary and sufficient conditions for left invertibility and uniform left invertibility under some weak additional hypotheses. A few examples are presented to illustrate the application of the proposed method.

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“…Finally, if communication were analog, one might assume a distorted version of the transmitted signal is always received without loss or delay. While this formulation is of considerable theoretical interest [28,35], we will not discuss it further because control with analog communication is so uncommon in current engineering practice.…”

Section: Nnrtsmentioning

confidence: 99%