01862nas a2200157   4500008004100000245008300041210006900124300001600193520130000209653002101509653001301530100001501543700001501558700001501573856011601588       2008                        eng d00aLeft invertibility of discrete systems with finite inputs and quantized output0 aLeft invertibility of discrete systems with finite inputs and qu  a4687 - 46923 a<p>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.</p>
10aEmbedded Control10aRobotics1 aDubbini, N1 aPiccoli, B1 aBicchi, A.  uhttp://95.110.227.47/publications/left-invertibility-discrete-systems-finite-inputs-and-quantized-output.html-0