01558nas a2200157 4500008004100000245007800041210006900119300001400188490000700202520100400209653002101213653001301234100001501247700001501262856012301277 2005 eng d00aControl synthesis for practical stabilization of quantized linear systems0 aControl synthesis for practical stabilization of quantized linea a397–4100 v633 a

In this work we face the stability problem for quantized control systems (QCS). A discrete–time single–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–invariant sets are reviewed and a lower bound on the size of invariant sets is provided.

10aEmbedded Control10aRobotics1 aPicasso, B1 aBicchi, A. uhttp://www.centropiaggio.unipi.it/publications/control-synthesis-practical-stabilization-quantized-linear-systems.html01667nas a2200169 4500008004100000245009300041210006900134300001400203520104000217653002101257653001301278100001501291700001601306700001501322700001901337856014101356 2004 eng d00aControl of Distributed Embedded Systems in the Presence of Unknown–but–Bounded Noise0 aControl of Distributed Embedded Systems in the Presence of Unkno a1448-14533 a

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.

10aEmbedded Control10aRobotics1 aPicasso, B1 aPalopoli, L1 aBicchi, A.1 aJohansson, K H uhttp://www.centropiaggio.unipi.it/publications/control-distributed-embedded-systems-presence-unknown%E2%80%93%E2%80%93bounded-noise.html01663nas a2200169 4500008004100000245008500041210006900126260001300195300001200208520106100220653002101281653001301302100001501315700001801330700001501348856013001363 2002 eng d00aConstruction of invariant and attractive sets for quantized-input linear systems0 aConstruction of invariant and attractive sets for quantizedinput cDecember a824-8293 a

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.

10aEmbedded Control10aRobotics1 aPicasso, B1 aGouaisbaut, F1 aBicchi, A. uhttp://www.centropiaggio.unipi.it/publications/construction-invariant-and-attractive-sets-quantized-input-linear-systems.html