Symbolic models for incrementally stable switched systems with aperiodic time sampling

Abstract

In this paper, we consider the problem of symbolic model design for the class of incrementally stable switched systems. Contrarily to the existing results in the literature where switching is considered as periodically controlled, in this paper, we consider aperiodic time sampling resulting either from uncertain or event-based sampling mechanisms. Firstly, we establish sufficient conditions ensuring that usual symbolic models computed using periodic time-sampling remain approximately bisimilar to a switched system when the sampling period is uncertain and belongs to a given interval; estimates on the bounds of the interval are provided. Secondly, we propose a new method to compute symbolic models related by feedback refinement relations to incrementally stable switched systems, using an event-based approximation scheme. For a given precision, these event-based models are guaranteed to enable transitions of shorter duration and are likely to allow for more reactiveness in controller design. Finally, an example is proposed in order to illustrate the proposed results and simulations are performed for a Boost dc-dc converter structure.

Guaranteed Control Synthesis for Continuous Systems in Uppaal Tiga

“…We plan on developing a time robust Euler scheme, which would guarantee that if the switch does not occur simultaneously, safety is still ensured. Note that this issue has already been studied in the literature in different frameworks, an interested reader might refer to [14,15].…”

Safety controller design for incrementally stable switched systems using event-based symbolic models

“…For a desired precision ε > 0 and a chosen state sampling parameter η satisfying (11), the transitions durations can be computed numerically while computing the symbolic model since they correspond to the values of τ ∈ T N τ * for which the function g changes sign. Contrarily to the event-based scheme for symbolic models design proposed in [8] where the symbolic model is designed while choosing only transitions of shorter durations, the proposed symbolic model proposed above provides all the transitions with durations τ ∈ T N τ * satisfying (9)- (10).…”

“…First of all, we provide a novel event-based scheme for symbolic models design. Contrarily to the event-based symbolic approach proposed in [8] where only transitions of shorter durations are considered, here the symbolic model is computed while considering all transitions of different durations satisfying a triggering condition. In this paper, we show that the obtained symbolic abstraction is related to the original switched system by a feedback refinement relation [11] and is thus useful for control applications.…”

Compositional Abstractions of Interconnected Discrete-Time Switched Systems

“…The work by [6] provides a finite abstraction that is related to the original incrementally stable switched system by establishing an approximate bisimulation relation between them. Recently, the result in [6] has been extended to the case of multi-rate symbolic models in [7], multi-scale symbolic models in [8], and to switched systems with aperiodic time sampling in [9].…”