@article {PB04-rendi, title = {Control synthesis for practical stabilization of quantized linear systems}, journal = {Rend. Sem. Mat. Univ. Pol. Torino, Control Theory and Stabil., I}, volume = {63}, number = {4}, year = {2005}, pages = {397{\textendash}410}, abstract = {

In this work we face the stability problem for quantized control systems (QCS). A discrete{\textendash}time single{\textendash}input linear model is considered and, motivated by technological applications, we assume that a uniform quantization of the control set is a priori fixed. As it is well known, for QCS only practical stability properties can be achieved, therefore we focus on the existence and construction of quantized controllers capable of steering a system to within invariant neighborhoods of the equilibrium. The main contribution of the paper consists in a theorem which provides a condition for the practical stabilization in a fixed number of steps: not only the result is interesting in itself, but also it enables to construct a family of stabilizing controllers by means of Model Predictive Control (MPC) techniques. In the last part of the paper some results on the characterization of controlled{\textendash}invariant sets are reviewed and a lower bound on the size of invariant sets is provided.

}, keywords = {Embedded Control, Robotics}, author = {B. Picasso and A. Bicchi} } @conference {PPBJ04, title = {Control of Distributed Embedded Systems in the Presence of Unknown{\textendash}but{\textendash}Bounded Noise}, booktitle = {Proc. IEEE Int. Conf. on Decision and Control}, year = {2004}, pages = {1448-1453}, abstract = {

In this paper we consider the problem of controlling multiple scalar systems through a limited capacity shared channel. Each system is affected by process noise and can be controlled byactuators with values in a {\em fixed}inite set. The control objective is to bound the evolution of the systems in specified sets (controlled invariance). Our goal is to find an optimal allocation of the shared communication resource to the different control activities and to identify correct choices for the design parameters. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. Namely, we give a feasibility criterion to decide whether a set of design parameters conforms with a control specification (i.e., with the controlled invariance of a specified set for each system). Moreover, we offer the explicit computation of the minimum bit rate necessary for the controlled invariance of a set, which is of utmost importance for solving the optimization problem.

}, keywords = {Embedded Control, Robotics}, author = {B. Picasso and L. Palopoli and A. Bicchi and K. H. Johansson} } @conference {PGB02, title = {Construction of invariant and attractive sets for quantized-input linear systems}, booktitle = {Proc. IEEE Int. Conf. on Decision and Control}, year = {2002}, month = {December}, pages = {824-829}, abstract = {

In this paper, the problem of the stabilization of a discrete-time linear system subject to a fixed and uniformly quantized control set is considered. It is well known that, working with quantized inputs, the states of the system (except for a negligible set of initial conditions) cannot reach asymptotically the equilibrium point. Our aim is then to find an invariant and attractive neighborhood of the equilibrium and provide with a controller which steers the system into it. We construct a continuous and increasing family of invariant sets including one which is, in a specific sense, minimal. The invariance and attractivity properties of such sets are revised in the finite control set case: we propose a family of controllers taking on a finite number of values and ensuring the system convergence to the minimal invariant set. Some consequences of our technique are underlined with particular regard to the usage of Model Predictive Control tools. In the last section an example which shows the effectiveness of our results is presented.

}, keywords = {Embedded Control, Robotics}, author = {B. Picasso and F. Gouaisbaut and A. Bicchi} }