After defining a notion of epsilon-density, we provide for any integer m>1 and real algebraic number alpha an estimate of the smallest epsilon such that the set of vectors of the form (t,t^alpha,...,t alpha^{m-1}) for tR is epsilon-dense modulo 1 in terms of the multiplicative Mahler measure M(A(x)) of the minimal integral polynomial A(x) of alpha, which is independent of m. In particular, we show that if alpha has degree d it is possible to take epsilon = 2^{[d/2]}/M(A(x)). On the other side we show using asymptotic estimates for Toeplitz determinants that we cannot have epsilon$-density for sufficiently large m whenever epsilon is strictly smaller than 1/M(A(x)). In the process of proving this we obtain a result of independent interest about the structure of the Z-module of integral linear recurrences of fixed length determined by a non-monic polynomial.
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.
This paper investigates the issue of how to make decentralised networks amenable to external control, i.e. how to ensure that they are appropriately organised so that they can be effectively
In this paper, we present a methodology for designing embedded controllers based on the so-called anytime control paradigm. A control law is split into a sequence of subroutine calls, each one fulfilling a control goal and refining the result produced by the previous one. We propose a design methodology to define a feedback controller structured in accordance with this paradigm and show how a switching policy of selecting the controller subroutines can be designed that provides stability guarantees for the closed-loop system. The cornerstone of this construction is a stochastic model describing the probability of executing, in each activation of the controller, the different subroutines. We show how this model can be constructed for realistic real-time task sets and provide an experimental validation of the approach.
In this paper we consider the problem of maneuvering an autonomous robot in complex unknown environments using vision. The goal is to accurately servo a wheeled vehicle to a desired posture using only feedback from an on-board camera, taking into account the nonholonomic nature of the vehicle kinematics and the limited field-ofview of the camera. With respect to existing visual servoing schemes, which achieve similar goals locally (i.e. when the desired and actual camera views are sufficiently similar), we propose a method to visually navigate the robot through an extended visual map before eventually reaching the desired goal. The map comprises a set of images, previously stored in an exploratory phase, that convey both topological and metric information regarding the connectivity through feasible robot paths and the geometry of the environment, respectively. Experimental results on a laboratory setup are reported showing the practicality of the proposed approach.
Interaction with the external world requires the ability to perceive dynamic changes in complex sensorial input and react promptly. Here we show that perception of dynamic stimuli in the visual and tactile sensory modalities share fundamental psychophysical aspects that can be explained by similar computational models. In vision, optic flow provides information on relative motion between the individual and the content of percept. For instance, radial patterns of optic flow are used to estimate time before contact with an approaching object4. Similarly, in the tactile modality, radial patterns of stimuli provide information on softness of probed objects3. Optic flow is also invoked to explain several visual illusions, including the well-known "barber-pole" effect10. Here we introduce a computational model of tactile flow, which is intimately related to existing models for the visual counterpart. The model accounts for psychophysical aspects of dynamic tactile perception and predicts illusory phenomena in the tactile domain, analogous to the barber-pole effect. When subjects touched translating pads with differently oriented gratings, they perceived a direction of motion that was significantly biased towards the orientation of the gratings. Therefore, these findings indicate that visual and tactile flow share similarities at the psychophysical and computational level and may be intended for similar perceptive goals. Results of this analysis have impact on the engineering of better haptic and multimodal interfaces for human-computer interaction.
Quantized linear systems are a widely studied class of nonlinear dynamics resulting from the control of a linear system through finite inputs. The stabilization problem for these models shall be studied in terms of the so called practical stability notion that essentially consists in confining the trajectories into sufficiently small neighborhoods of the equilibrium (ultimate boundedness) . In this paper, we study the problem of describing the smallest sets into which any feedback can ultimately confine the state, for a given linear single-input system with an assigned finite set of admissible input values (quantization). We show that a controlled invariant set of minimal size is contained in a family of sets (namely, hypercubes in controller-canonical form), previously introduced in [14, 15] . A comparison is presented which quantifies the improvement in tightness of the proposed analysis technique with respect to classical results using quadratic Lyapunov functions.
In this paper, we describe a biomimetic-fabric-based sensing glove that can be used tomonitor hand posture and gesture. Our device is made of a distributed sensor network of piezoresistive conductive elastomers integrated into an elastic fabric. This solution does not affect natural movement and hand gestures, and can be worn for a long time with no discomfort. The glove could be fruitfully employed in behavioral and functional studies with functional MRI (fMRI) during specific tactile or motor tasks. To assess MR compatibility of the system, a statistical test on phantoms is introduced. This test can also be used for testing the compatibility of mechatronic devices designed to produce different stimuli inside the MR environment. We propose a statistical test to evaluate changes in SNR and time-domain standard deviations between image sequences acquired under different experimental conditions. fMRI experiments on subjects wearing the glove are reported. The reproducibility of fMRIresults obtained with andwithout the glove was estimated. A good similarity between the activated regions was found in the two conditions.
Component-based techniques revolve around composable, reusable software objects that shield the application level software from the details of the hardware and lowlevel software implementation and vice versa. Components provide many benefits that have led to their wide adoption in software and middleware developed for embedded systems: They are well-defined entities that can be replaced without affecting the rest of the systems, they can be developed and tested separately and integrated later, and they are reusable. Clearly such features are important for the design of large-scale complex systems more generally, beyond software architectures. We propose the use of a component approach to address embedded control problems. We outline a general componentbased framework to embedded control and show how it can be instantiated in specific problems that arise in the control over/of sensor networks. Building on the middleware component framework developed under the European project RUNES, we develop a number of control-oriented components necessary for the implementation of control applications and design their integration. The paper provides the overview of the approach, discusses a real life application where the approach has been tested and outlines a number of specific control problems that arise in this application.
