01777nas a2200169   4500008004100000245008300041210006900124300001400193490000700207520120000214653002101414653001301435100001501448700001501463700001501478856011401493       2010                        eng d00aLeft invertibility of discrete systems with finite inputs and quantized output0 aLeft invertibility of discrete systems with finite inputs and qu  a798 - 8090 v833 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 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.</p>
10aEmbedded Control10aRobotics1 aDubbini, N1 aPiccoli, B1 aBicchi, A.  uhttp://95.110.227.16/publications/left-invertibility-discrete-systems-finite-inputs-and-quantized-output.html