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Left invertibility of discrete systems with finite inputs and quantized output

Dubbini, Nevio and Piccoli, Benedetto and Bicchi, Antonio (2008) Left invertibility of discrete systems with finite inputs and quantized output. In: 47th IEEE Conference on Decision and Control, 9-11 dicembre 2008, Cancun, Mexico.

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    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.

    Item Type: Conference or Workshop Item (Paper)
    Uncontrolled Keywords: Left invertibility, nonlinear control systems, quantized systems, Iterated Function Systems, fractals
    Subjects: Area01 - Scienze matematiche e informatiche > MAT/03 - Geometria
    Depositing User: Ph.D. Nevio Dubbini
    Date Deposited: 13 Sep 2010
    Last Modified: 20 Dec 2010 11:45
    URI: http://eprints.adm.unipi.it/id/eprint/734

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