@article {DPB10, title = {Left invertibility of discrete systems with finite inputs and quantized output}, journal = {International Journal Of Control}, volume = {83}, number = {4}, year = {2010}, pages = {798 - 809}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {N. Dubbini and B. Piccoli and A. Bicchi} } @conference {DPB-CDC08, title = {Left invertibility of discrete systems with finite inputs and quantized output}, booktitle = {Proc. IEEE Int. Conf. on Decision and Control}, year = {2008}, pages = {4687 - 4692}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {N. Dubbini and B. Piccoli and A. Bicchi} } @conference {GFBP-07, title = {Steering Dynamical Systems with Finite Plans and Limited Path Length}, booktitle = {European Control Conference}, year = {2007}, pages = {4686-4690}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {L. Greco and A. Fagiolini and A. Bicchi and B. Piccoli} } @article {BBMP-TAC06, title = {Feedback Encoding for Efficient Symbolic Control of Dynamical Systems}, journal = {IEEE Trans. on Automatic Control}, volume = {51}, number = {6}, year = {2006}, pages = {1-16}, abstract = {

The problem of efficiently steering dynamical systems by generating finite input plans is considered. Finite plans are finite{\textendash}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.

}, keywords = {Embedded Control, Robotics}, author = {A. Bicchi and A. Marigo and B. Piccoli} } @conference {BMP06-HSCC, title = {Improving efficiency of finite plans by optimal choice of input sets}, booktitle = {Hybrid Systems: Computation and Control}, series = {Lecture Notes in Computer Science}, volume = {3927 / 2006}, year = {2006}, pages = {108-122}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, abstract = {

Finite plans proved to be an efficient method to steer complex control systems via feedback quantization. Such finite plans can be encoded by finite{\textendash}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.

}, keywords = {Embedded Control, Robotics}, author = {A. Bicchi and A. Marigo and B. Piccoli}, editor = {J. Hespanha and A. Tiwari} } @conference {FGBPM06, title = {Symbolic Control for Underactuated Differentially Flat Systems}, booktitle = {Proc. IEEE Int. Conf. on Robotics and Automation}, year = {2006}, pages = {1649-1654}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {A. Fagiolini and L. Greco and A. Bicchi and B. Piccoli and A. Marigo} } @conference {ABBPSZ05, title = {Randomized Algorithms for Platform{\textendash}based Design}, booktitle = {Proc. IEEE Int. Conf. on Decision and Control}, year = {2005}, pages = {6638 - 6643}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {A. Agostini and A. Balluchi and A. Bicchi and B. Piccoli and Sangiovanni Vincentelli, A. and K. Zadarnowska} } @conference {BMP04, title = {Discrete and Hybrid Nonholonomy}, booktitle = {Hybrid Systems: Computation and Control}, series = {LNCS}, volume = {2993}, number = {157{\textendash}172}, year = {2004}, pages = {157-172}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {A. Bicchi and A. Marigo and B. Piccoli}, editor = {R. Alur and G. Pappas} } @conference {BMP03, title = {Encoding steering control with symbols}, booktitle = {Proc. IEEE Int. Conf. on Decision and Control}, year = {2003}, pages = {3343-3348}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {A. Bicchi and A. Marigo and B. Piccoli} } @conference {MPB02, title = {A Group-Theoretic Characterization of Quantized Control Systems}, booktitle = {Proc. IEEE Int. Conf. on Decision and Control}, year = {2002}, month = {December}, pages = {811-816}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {A. Marigo and B. Piccoli and A. Bicchi} } @article {BMP02, title = {On the reachability of quantized control systems}, journal = {IEEE Trans. on Automatic Control}, volume = {4}, number = {47}, year = {2002}, month = {April}, pages = {546-563}, abstract = {

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.

}, keywords = {Embedded Control, Robotics}, author = {A. Bicchi and A. Marigo and B. Piccoli} }