Università di Pisa
Sistema bibliotecario di ateneo

Left invertibility of discrete systems with finite inputs and quantized output

Dubbini, Nevio and Piccoli, Benedetto and Bicchi, Antonio (2010) Left invertibility of discrete systems with finite inputs and quantized output. International Journal of Control, 83 (4). pp. 798-809. ISSN 1366-5820

[img] PDF
Restricted to Repository staff only until 01 April 2011.

Download (1365Kb)


    The aim of this paper is to address left invertibility for dynamical systems with inputs and outputs in discrete sets. We study systems which 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. Our main results are obtained under some contractivity hypotheses. 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 invertibility property of the system. Our main result is a necessary and sufficient condition for left invertibility and uniform left invertibility for joint contractive systems. In addition, an algorithm is proposed to recover inputs from output strings. A few examples are presented to illustrate the application of the proposed method.

    Item Type: Article
    Uncontrolled Keywords: Left invertibility, nonlinear control systems, quantized systems, Iterated Function Systems, contractive systems
    Subjects: Area01 - Scienze matematiche e informatiche > MAT/03 - Geometria
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI MATEMATICA "L. TONELLI"
    Depositing User: Ph.D. Nevio Dubbini
    Date Deposited: 06 Sep 2010
    Last Modified: 27 Dec 2010 13:53
    URI: http://eprints.adm.unipi.it/id/eprint/736

    Repository staff only actions

    View Item