01672nas a2200169 4500008004100000245010100041210006900142260001700211300001400228490000700242520107300249653001301322100001501335700001501350700001501365856012201380 2011 eng d00aLeft invertibility of discrete-time output-quantized systems: the linear case with finite inputs0 aLeft invertibility of discretetime outputquantized systems the l cNovember, 16 a117 - 1390 v233 a

This paper studies left invertibility of discrete-time linear outputquantized systems. Quantized outputs are generated according to a given partition of the state-space, while inputs are sequences on a nite alphabet. Left invertibility, i.e. injectivity of I/O map, is reduced to left D-invertibility, under suitable conditions. While left invertibility takes into account membership to sets of a given partition, left D-invertibility considers only membership to a single set, and is much easier to detect. The condition under which left invertibility and left D-invertibility are equivalent is that the elements of the dynamic matrix of the system form an algebraically independent set. Our main result is a method to compute left D-invertibility (so also left invertibility for a full measure matrix set) for all linear systems with no eigenvalue of modulus one. Therefore we are able to check left invertibility of output-quantized linear systems for a full measure matrices set. Some examples are presented to show the application of the proposed method.

10aRobotics1 aDubbini, N1 aPiccoli, B1 aBicchi, A. uhttp://95.110.227.16/publications/left-invertibility-discrete-time-output-quantized-systems-linear-case-finite-inputs01777nas 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

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.

10aEmbedded Control10aRobotics1 aDubbini, N1 aPiccoli, B1 aBicchi, A. uhttp://95.110.227.16/publications/left-invertibility-discrete-systems-finite-inputs-and-quantized-output.html01862nas 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

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.

10aEmbedded Control10aRobotics1 aDubbini, N1 aPiccoli, B1 aBicchi, A. uhttp://95.110.227.16/publications/left-invertibility-discrete-systems-finite-inputs-and-quantized-output.html-0