Showing papers by "Paulo Tabuada published in 2006"

Linear Time Logic Control of Discrete-Time Linear Systems

Abstract: The control of complex systems poses new challenges that fall beyond the traditional methods of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several interacting submodules within a system. The desired objectives are no longer captured by usual control specifications such as stabilization or output regulation. Instead, we consider specifications given by linear temporal logic (LTL) formulas. We show that existence of controllers for discrete-time controllable linear systems and LTL specifications can be decided and that such controllers can be effectively computed. The closed-loop system is of hybrid nature, combining the original continuous dynamics with the automatically synthesized switching logic required to enforce the specification

Preliminary results on state-trigered scheduling of stabilizing control tasks

Abstract: In this paper we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler should be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. According to this feedback paradigm, the decision of executing control tasks should not be based on release times and deadlines but rather on the state of the plant. We investigate the feasibility of a simple state triggered scheduler based on the state norm and provide some schedulability results

On the stability of zeno equilibria

Abstract: Zeno behaviors are one of the (perhaps unintended) features of many hybrid models of physical systems. They have no counterpart in traditional dynamical systems or automata theory and yet they have remained relatively unexplored over the years. In this paper we address the stability properties of a class of Zeno equilibria, and we introduce a necessary paradigm shift in the study of hybrid stability. Motivated by the peculiarities of Zeno equilibria, we consider a form of asymptotic stability that is global in the continuous state, but local in the discrete state. We provide sufficient conditions for stability of these equilibria, resulting in sufficient conditions for the existence of Zeno behavior.

Approximate Reduction of Dynamical Systems

Abstract: The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction is typically performed in an "exact" manner - as is the case with mechanical systems with symmetry - which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples

Symbolic control of linear systems based on symbolic subsystems

Abstract: This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification.

Networked embedded sensing and control : Workshop NESC'05 : University of Notre Dame, USA, October 2005 proceedings

Abstract: Part I Multi-Agent Control.- Part II Simulation and Implementation.- Part III Distributed Sensing, Filtering and Estimation.- Part IV Control over Networks I.- Part V Control over Networks II.

On the stability of zeno equilibria

Abstract: Zeno behaviors are one of the (perhaps unintended) features of many hybrid models of physical systems. They have no counterpart in traditional dynamical systems or automata theory and yet they have remained relatively unexplored over the years. In this paper we address the stability properties of a class of Zeno equilibria, and we introduce a necessary paradigm shift in the study of hybrid stability. Motivated by the peculiarities of Zeno equilibria, we consider a form of asymptotic stability that is global in the continuous state, but local in the discrete state. We provide sufficient conditions for stability of these equilibria, resulting in sufficient conditions for the existence of Zeno behavior.

Symbolic Control of Linear Systems Based on

Abstract: This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representa- tions of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification. model can be used in another model. Analysis/design could then be performed on simpler models thereby reducing the complexity of these tasks. In this paper, we take important steps along this direction by focusing on the control of continuous time systems based on symbolic models. In particular, we are interested in finite state models capturing the essential properties of linear control sys- tems. The finite state nature of these models is important for two main reasons. First, finite state models are especially well suited for automated analysis and design which is becoming in- creasingly important given the size of nowadays complex con- trol systems. The use of such models thus opens new algorithmic perspectives for analysis and design. Second, finite state models offer a common language to describe an abstract view of con- tinuous dynamics as well as the software implementation of control algorithms. It is, therefore, possible to formally reason about the behavior of the interconnection between continuous dynamics and software which has been one of the main thrusts behind the research area of hybrid systems. With the objective of strengthening this connection between continuous models of dynamics and finite state models of software we will focus, in this paper, on a particular symbolic model for control systems: symbolic subsystems. B. Contributions