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.

VL - 23 N1 -published online 8 Sept. 2011

ER - TY - JOUR T1 - Left invertibility of discrete systems with finite inputs and quantized output JF - International Journal Of Control Y1 - 2010 A1 - N. Dubbini A1 - B. Piccoli A1 - A. Bicchi KW - Embedded Control KW - Robotics AB -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.

VL - 83 ER - TY - ABST T1 - Sensor Deployment for Network-like Environments Y1 - 2010 A1 - L. Greco A1 - M. Gaeta A1 - B. Piccoli KW - Robotics N1 -Full version

ER - TY - JOUR T1 - Sensor Deployment for Network-like Environments JF - IEEE Trans. on Automat. Contr. Y1 - 2010 A1 - L. Greco A1 - M. Gaeta A1 - B. Piccoli KW - Robotics N1 -Condit. accepted as Technical Note

ER - TY - CONF T1 - Deployment of sensors in a network-like environment T2 - Proc. 47th IEEE Conference on Decision and Control Y1 - 2008 A1 - L. Greco A1 - M. Gaeta A1 - B. Piccoli KW - Robotics JF - Proc. 47th IEEE Conference on Decision and Control CY - Cancun, Mexico ER - TY - CONF T1 - Left invertibility of discrete systems with finite inputs and quantized output T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2008 A1 - N. Dubbini A1 - B. Piccoli A1 - A. Bicchi KW - Embedded Control KW - Robotics AB -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.

JF - Proc. IEEE Int. Conf. on Decision and Control ER - TY - CONF T1 - Steering Dynamical Systems with Finite Plans and Limited Path Length T2 - European Control Conference Y1 - 2007 A1 - L. Greco A1 - A. Fagiolini A1 - A. Bicchi A1 - B. Piccoli KW - Embedded Control KW - Robotics AB -Complex 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.

JF - European Control Conference ER - TY - JOUR T1 - Feedback Encoding for Efficient Symbolic Control of Dynamical Systems JF - IEEE Trans. on Automatic Control Y1 - 2006 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli KW - Embedded Control KW - Robotics AB -The 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.

VL - 51 ER - TY - CONF T1 - Improving efficiency of finite plans by optimal choice of input sets T2 - Hybrid Systems: Computation and Control Y1 - 2006 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli ED - J. Hespanha ED - A. Tiwari KW - Embedded Control KW - Robotics AB -Finite 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.

JF - Hybrid Systems: Computation and Control T3 - Lecture Notes in Computer Science PB - Springer-Verlag VL - 3927 / 2006 ER - TY - CONF T1 - Symbolic Control for Underactuated Differentially Flat Systems T2 - Proc. IEEE Int. Conf. on Robotics and Automation Y1 - 2006 A1 - A. Fagiolini A1 - L. Greco A1 - A. Bicchi A1 - B. Piccoli A1 - A. Marigo KW - Embedded Control KW - Robotics AB -In 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.

JF - Proc. IEEE Int. Conf. on Robotics and Automation ER - TY - CONF T1 - Randomized Algorithms for Platform–based Design T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2005 A1 - A. Agostini A1 - A. Balluchi A1 - A. Bicchi A1 - B. Piccoli A1 - Sangiovanni Vincentelli, A. A1 - K. Zadarnowska KW - Embedded Control KW - Robotics AB -The 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.

JF - Proc. IEEE Int. Conf. on Decision and Control ER - TY - CONF T1 - Discrete and Hybrid Nonholonomy T2 - Hybrid Systems: Computation and Control Y1 - 2004 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli ED - R. Alur ED - G. Pappas KW - Embedded Control KW - Robotics AB -In 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.

JF - Hybrid Systems: Computation and Control T3 - LNCS PB - Springer-Verlag VL - 2993 ER - TY - CONF T1 - Encoding steering control with symbols T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2003 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli KW - Embedded Control KW - Robotics AB -In 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.

JF - Proc. IEEE Int. Conf. on Decision and Control ER - TY - CONF T1 - A Group-Theoretic Characterization of Quantized Control Systems T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2002 A1 - A. Marigo A1 - B. Piccoli A1 - A. Bicchi KW - Embedded Control KW - Robotics AB -In 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.

JF - Proc. IEEE Int. Conf. on Decision and Control ER - TY - JOUR T1 - On the reachability of quantized control systems JF - IEEE Trans. on Automatic Control Y1 - 2002 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli KW - Embedded Control KW - Robotics AB -In 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.

VL - 4 ER - TY - CONF T1 - Quantized Control Systems and Discrete Nonholonomy T2 - Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control Y1 - 2000 A1 - A. Bicchi A1 - A. Marigo A1 - B. Piccoli KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems KW - Quantized Control Systems JF - Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control PB - Elsevier CY - Princeton, NJ, USA ER - TY - CONF T1 - Reachability Analysis for a Class of Quantized Control Systems T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2000 A1 - A. Marigo A1 - B. Piccoli A1 - A. Bicchi KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems KW - Quantized Control Systems JF - Proc. IEEE Int. Conf. on Decision and Control CY - Sydney, AU ER - TY - CONF T1 - Stability and Robustness of Optimal Synthesis for Route Tracking by Dubins' Vehicles T2 - Proc. 39th IEEE Conference on Decision and Control Y1 - 2000 A1 - A. Balluchi A1 - A. Bicchi A1 - B. Piccoli A1 - P. Souères KW - Autonomous Vehicles KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems JF - Proc. 39th IEEE Conference on Decision and Control CY - Sydney, Australia VL - 1 N1 -(invited paper)

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