A discrete-event model of asynchronous quantised systems

Förstner, D.; Jung, Merten; Lunze, Jan

doi:10.1016/s0005-1098(02)00023-7

Cited by 27 publications

(21 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More complex continuous dynamics, but simpler discrete dynamics, were considered in [AHLP00], where it was shown that o-minimal hybrid systems also admit symbolic models. Symbolic models for control systems were only considered later and early results were reported in [KASL00,MRO02,FJL02,CW98]. More precise results appeared recently in [TP06,Tab07b] where it was shown that discrete-time controllable linear systems admit symbolic models.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations

Pola¹,

Tabuada²

2009

SIAM J. Control Optim.

141

189

View full text Add to dashboard Cite

Abstract. Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating complexity in control design. In fact, symbolic models enable the use of well known algorithms in the context of supervisory control and algorithmic game theory, for controller synthesis. Since the 1990's many researchers faced the problem of identifying classes of dynamical and control systems that admit symbolic models. In this paper we make a further progress along this research line by focusing on control systems affected by disturbances. Our main contribution is to show that incrementally globally asymptotically stable nonlinear control systems with disturbances admit symbolic models. When specializing these results to linear systems, we show that these symbolic models can be easily constructed.

show abstract

Section: Introductionmentioning

confidence: 99%

Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations

Pola¹,

Tabuada²

2009

SIAM J. Control Optim.

141

189

View full text Add to dashboard Cite

show abstract

“…Related work To the best of our knowledge, the contribution of the paper is new. Control of hybrid systems using finitestate approximation is a classical topic, Alur et al (2000); Gonzalez et al (2001); Chutinan and Krogh (2003) ;Förstnera et al (2002); Moor et al (2002); Koutsoukos et al (2000). The main difference with respect to Gonzalez et al (2001); Chutinan and Krogh (2003); Koutsoukos et al (2000) is the presence of partial observations, that the generation of events is not synchronous with inputs, and that the hybrid plant contains reset maps.…”

Section: Introductionmentioning

confidence: 99%

“…The main difference with respect to Gonzalez et al (2001); Chutinan and Krogh (2003); Koutsoukos et al (2000) is the presence of partial observations, that the generation of events is not synchronous with inputs, and that the hybrid plant contains reset maps. With respect to Förstnera et al (2002); Moor et al (2002) the main differences are that we consider hybrid systems as opposed to continuous ones, and we address partial observations. In addition, we do not propose a general purpose finitestate abstraction, rather the proposed abstraction is intended as a vehicle for solving the specific control problem.…”

Section: Introductionmentioning

confidence: 99%

“…In Chutinan and Krogh (2003); Koutsoukos et al (2000); Alur et al (2000); Fainekos et al (2007); Belta et al (2005); Philips et al (2003) the finite-state abstraction is computed by dividing the state-space of the system into regions. In Förstnera et al (2002); Moor et al (2002); Raisch and O'Young (1995); Moor et al (2002); Moor and Raisch (1999); Raisch (2000), the abstraction of the system is constructed by storing the output (or state) response of the system to input sequences of finite length. In contrast, here the abstraction is obtained by sampling the hybrid system in time, not by discretizing it in space.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sampled-data control of hybrid systems with discrete inputs and outputs

Petreczky

Collins

Beek

et al. 2009

IFAC Proceedings Volumes

View full text Add to dashboard Cite

We address the control synthesis of hybrid systems with discrete inputs, disturbances and outputs. The control objective is to ensure that the events of the closed-loop system belong to the language of the control requirements. The controller is sampling-based and it is representable by a finitestate machine. We formalize the control problem and provide a theoretically sound solution. The solution is based on solving a discrete-event control problem for a finite-state abstraction of the plant. We propose a specific construction for the finite-state abstraction. This construction is not based on discretizing the state-space, but rather on converting the continuous-time hybrid system to a discrete-time one based on sampling. The construction works only for a specific class of hybrid systems. We describe this class of systems and we provide an example of such a system, inspired by an industrial use-case.

show abstract

“…Other results in approximation theory for timed systems can be found e.g. in [6], [12]. To analyze temporal properties of hybrid automata, it is reasonable to consider as abstracting system the class of timed automata, that can generally be abstracted into finite state systems [3].…”

Section: Introductionmentioning

confidence: 99%

Approximate timed abstractions of hybrid automata

D’Innocenzo

Julius

Benedetto

et al. 2007

2007 46th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

Abstract-Given a hybrid automaton and a desired precision, we aim at constructing an approximate abstraction by means of a timed automaton, whose discrete state trajectories approximate the discrete state trajectories of the original system, with the desired precision on switching times. We show that using the Euclidian metric on reals it is not always possible to construct a timed automaton that is close to a hybrid automaton with finite precision. For this reason, we motivate and introduce relative metrics on reachability time, external language and simulation relation to quantify the precision of our abstraction. Our main result is to propose a novel algorithm to construct a timed automaton that is an approximate timed abstraction of a hybrid automaton with desired precision, and study its convergence properties. For an extended version of this paper refer to [11].

show abstract

A discrete-event model of asynchronous quantised systems

Cited by 27 publications

References 11 publications

Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations

Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations

Sampled-data control of hybrid systems with discrete inputs and outputs

Approximate timed abstractions of hybrid automata

Contact Info

Product

Resources

About