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://www.centropiaggio.unipi.it/publications/left-invertibility-discrete-time-output-quantized-systems-linear-case-finite-inputs01790nas a2200169 4500008004100000245008300041210006900124300001400193490000700207520120000214653002101414653001301435100001501448700001501463700001501478856012701493 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 aThe 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://www.centropiaggio.unipi.it/publications/left-invertibility-discrete-systems-finite-inputs-and-quantized-output.html00417nas a2200121 4500008004100000245005200041210005100093653001300144100001300157700001300170700001500183856009700198 2010 eng d00aSensor Deployment for Network-like Environments0 aSensor Deployment for Networklike Environments10aRobotics1 aGreco, L1 aGaeta, M1 aPiccoli, B uhttp://www.centropiaggio.unipi.it/publications/sensor-deployment-network-environments.html-000415nas a2200121 4500008004100000245005200041210005100093653001300144100001300157700001300170700001500183856009500198 2010 eng d00aSensor Deployment for Network-like Environments0 aSensor Deployment for Networklike Environments10aRobotics1 aGreco, L1 aGaeta, M1 aPiccoli, B uhttp://www.centropiaggio.unipi.it/publications/sensor-deployment-network-environments.html00492nas a2200145 4500008004100000245005600041210005500097260002900152300001600181653001300197100001300210700001300223700001500236856009500251 2008 eng d00aDeployment of sensors in a network-like environment0 aDeployment of sensors in a networklike environment aCancun, MexicocDecember a4257–426210aRobotics1 aGreco, L1 aGaeta, M1 aPiccoli, B uhttp://www.centropiaggio.unipi.it/publications/deployment-sensors-network-environment.html01875nas a2200157 4500008004100000245008300041210006900124300001600193520130000209653002101509653001301530100001501543700001501558700001501573856012901588 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 aThe 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://www.centropiaggio.unipi.it/publications/left-invertibility-discrete-systems-finite-inputs-and-quantized-output.html-001537nas a2200169 4500008004100000245007300041210006900114300001400183520095600197653002101153653001301174100001301187700001701200700001501217700001501232856012001247 2007 eng d00aSteering Dynamical Systems with Finite Plans and Limited Path Length0 aSteering Dynamical Systems with Finite Plans and Limited Path Le a4686-46903 aComplex dynamical systems can be steered by using symbolic input plans. These plans must have a finite descriptive length, and can be expressed by means of words chosen in an alphabet of symbols. In this way, such plans can be sent through a limited capacity channel to a remote system, where they are decoded in suitable control actions. The choice of this symbols is essential to efficiently encode steering plans. To this aim, in this paper, we state the problem of finding symbols maximizing the interval of points reachable by the system along paths with constrained length. We focus on the problem with two symbols, and compare the results with those produced by plans not accounting for the length constraint. Moreover, the behavior of a simple helicopter, steered by both kinds of plans, has been simulated, in order to illustrate the power of the overall control system, and to emphasize the improvements introduced by the new plans.

10aEmbedded Control10aRobotics1 aGreco, L1 aFagiolini, A1 aBicchi, A.1 aPiccoli, B uhttp://www.centropiaggio.unipi.it/publications/steering-dynamical-systems-finite-plans-and-limited-path-length.html01455nas a2200169 4500008004100000245007400041210006900115300000900184490000700193520088800200653002101088653001301109100001501122700001401137700001501151856011901166 2006 eng d00aFeedback Encoding for Efficient Symbolic Control of Dynamical Systems0 aFeedback Encoding for Efficient Symbolic Control of Dynamical Sy a1-160 v513 aThe problem of efficiently steering dynamical systems by generating finite input plans is considered. Finite plans are finite–length words constructed on a finite alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. Efficiency is considered in terms of the computational complexity of plans, and in terms of their description length (in number of bits). We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. The paper also investigates how the efficiency of planning is affected by the choice of inputs, and provides some results as to optimal performance in terms of accuracy and range.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B uhttp://www.centropiaggio.unipi.it/publications/feedback-encoding-efficient-symbolic-control-dynamical-systems.html01362nas a2200205 4500008004100000245007300041210006900114260002000183300001200203490001600215520070100231653002100932653001300953100001500966700001400981700001500995700001601010700001401026856011601040 2006 eng d00aImproving efficiency of finite plans by optimal choice of input sets0 aImproving efficiency of finite plans by optimal choice of input bSpringer-Verlag a108-1220 v3927 / 20063 aFinite plans proved to be an efficient method to steer complex control systems via feedback quantization. Such finite plans can be encoded by finite–length words constructed on suitable alphabets, thus permitting transmission on limited capacity channels. In particular flat systems can be steered computing arbitrarily close approximations of a desired equilibrium in polynomial time. The paper investigates how the efficiency of planning is affected by the choice of inputs, and provides some results as to optimal performance in terms of accuracy and range. Efficiency is here measured in terms of computational complexity and description length (in number of bits) of finite plans.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B1 aHespanha, J1 aTiwari, A uhttp://www.centropiaggio.unipi.it/publications/improving-efficiency-finite-plans-optimal-choice-input-sets.html01436nas a2200181 4500008004100000245006700041210006700108300001400175520084200189653002101031653001301052100001701065700001301082700001501095700001501110700001401125856011501139 2006 eng d00aSymbolic Control for Underactuated Differentially Flat Systems0 aSymbolic Control for Underactuated Differentially Flat Systems a1649-16543 aIn this paper we address the problem of generating input plans to steer complex dynamical systems in an obstacle-free environment. Plans considered admit a finite description length and are constructed by words on an alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. Moreover, we illustrate by simulations the power of the proposed method, solving the steering problem for two examples in the class of underactuated systems, which have attracted wide attention in the recent literature.

10aEmbedded Control10aRobotics1 aFagiolini, A1 aGreco, L1 aBicchi, A.1 aPiccoli, B1 aMarigo, A uhttp://www.centropiaggio.unipi.it/publications/symbolic-control-underactuated-differentially-flat-systems.html01449nas a2200193 4500008004100000245005400041210005400095300001600149520083600165653002101001653001301022100001601035700001601051700001501067700001501082700003101097700001901128856010801147 2005 eng d00aRandomized Algorithms for Platform–based Design0 aRandomized Algorithms for Platform–based Design a6638 - 66433 aThe design of automotive control systems is becoming increasingly complex as the level of performance required by car manufactures grows continuously and the constraints on cost and development time imposed by the market become tighter. A successful design, without costly and time consuming re-design cycles, can be achieved only by using an efficient design methodology that allows for component re-use and evaluation of platform requirements at the early stages of the design flow. In this paper, we illustrate a control-implementation design methodology for the development of embedded controllers by composition of algorithms picked up from libraries. Randomized algorithms and hybrid system theory are used to develop techniques for functional and architecture evaluations, which are implemented in a prototype tool.

10aEmbedded Control10aRobotics1 aAgostini, A1 aBalluchi, A1 aBicchi, A.1 aPiccoli, B1 aSangiovanni Vincentelli, A1 aZadarnowska, K uhttp://www.centropiaggio.unipi.it/publications/randomized-algorithms-platform%E2%80%93based-design.html01260nas a2200205 4500008004100000245003600041210003600077260002000113300001200133490000900145520070800154653002100862653001300883100001500896700001400911700001500925700001200940700001400952856008800966 2004 eng d00aDiscrete and Hybrid Nonholonomy0 aDiscrete and Hybrid Nonholonomy bSpringer-Verlag a157-1720 v29933 aIn this paper we consider the generalization of the classical notion of nonholonomy of smooth constraints in analytical mechanics, to a substantially wider set of systems, allowing for discrete and hybrid (mixed continuous and discrete) configurations and transitions. We show that the general notion of nonholonomy can be captured by the definition of two different types of nonholonomicbehaviours, which we call {\em internal}nd {\em external}, respectively. Examples are reported of systems exhibiting either the former only, or the latter only, or both. For some classes of systems, we provide equivalent or sufficient characterizations of such definitions, which allow for practical tests.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B1 aAlur, R1 aPappas, G uhttp://www.centropiaggio.unipi.it/publications/discrete-and-hybrid-nonholonomy.html01245nas a2200157 4500008004100000245004300041210004300084300001400127520077800141653002100919653001300940100001500953700001400968700001500982856009000997 2003 eng d00aEncoding steering control with symbols0 aEncoding steering control with symbols a3343-33483 aIn this paper, we consider the problem of steering complex dynamical systems among equilibria in their state space in efficient ways. Efficiency is considered as the possibility of compactly representing the (typically very large, or infinite) set of reachable equilibria and quickly computing plans to move among them. To this purpose, we consider the possibility of building lattice structures by purposefully introducing quantization of inputs. We consider different ways in which control actions can be encoded in a finite or numerable set of symbols, review different applications where symbolic encoding of control actions can be employed with success, and provide a unified framework in which to study the many different possible manifestations of the idea.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B uhttp://www.centropiaggio.unipi.it/publications/encoding-steering-control-symbols.html01158nas a2200169 4500008004100000245006800041210006500109260001300174300001200187520059600199653002100795653001300816100001400829700001500843700001500858856011500873 2002 eng d00aA Group-Theoretic Characterization of Quantized Control Systems0 aGroupTheoretic Characterization of Quantized Control Systems cDecember a811-8163 aIn this paper we consider the reachability problem for quantized control systems, i.e. systems that take inputs from a finite set of symbols. Previous work addressed this problem for linear systems and for some specific classes of nonlinear driftless systems. In this paper we attack the study of more general nonlinear systems. To do so we find it useful to pose the problem in more abstract terms, and make use of the wealth of tools available in group theory, which enables us to proceed in our agenda of better understanding effects of quantization of inputs on dynamic systems.

10aEmbedded Control10aRobotics1 aMarigo, A1 aPiccoli, B1 aBicchi, A. uhttp://www.centropiaggio.unipi.it/publications/group-theoretic-characterization-quantized-control-systems.html01271nas a2200181 4500008004100000245005300041210004600094260001000140300001200150490000600162520074800168653002100916653001300937100001500950700001400965700001500979856009500994 2002 eng d00aOn the reachability of quantized control systems0 areachability of quantized control systems cApril a546-5630 v43 aIn this paper we study control systems whose input sets are quantized, i.e. finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e. nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.

10aEmbedded Control10aRobotics1 aBicchi, A.1 aMarigo, A1 aPiccoli, B uhttp://www.centropiaggio.unipi.it/publications/reachability-quantized-control-systems.html00593nas a2200157 4500008004100000245005500041210005500096260003300151653004000184653003000224653003000254100001500284700001400299700001500313856010700328 2000 eng d00aQuantized Control Systems and Discrete Nonholonomy0 aQuantized Control Systems and Discrete Nonholonomy aPrinceton, NJ, USAbElsevier10aHybrid and Embedded Control Systems10aNonlinear Control Systems10aQuantized Control Systems1 aBicchi, A.1 aMarigo, A1 aPiccoli, B uhttp://www.centropiaggio.unipi.it/publications/quantized-control-systems-and-discrete-nonholonomy.html00638nas a2200169 4500008004100000245006700041210006700108260002500175300001400200653004000214653003000254653003000284100001400314700001500328700001500343856011000358 2000 eng d00aReachability Analysis for a Class of Quantized Control Systems0 aReachability Analysis for a Class of Quantized Control Systems aSydney, AUcDecember a3963-396810aHybrid and Embedded Control Systems10aNonlinear Control Systems10aQuantized Control Systems1 aMarigo, A1 aPiccoli, B1 aBicchi, A. uhttp://www.centropiaggio.unipi.it/publications/reachability-analysis-class-quantized-control-systems.html00727nas a2200193 4500008004100000245008900041210006900130260003200199300001000231490000600241653002400247653004000271653003000311100001600341700001500357700001500372700001600387856013000403 2000 eng d00aStability and Robustness of Optimal Synthesis for Route Tracking by Dubins' Vehicles0 aStability and Robustness of Optimal Synthesis for Route Tracking aSydney, AustraliacDecember a581-60 v110aAutonomous Vehicles10aHybrid and Embedded Control Systems10aNonlinear Control Systems1 aBalluchi, A1 aBicchi, A.1 aPiccoli, B1 aSouères, P uhttp://www.centropiaggio.unipi.it/publications/stability-and-robustness-optimal-synthesis-route-tracking-dubins-vehicles.html