Symbolic Supervisory Control of Infinite Transition Systems Under Partial Observation Using Abstract Interpretation

Abstract

We propose algorithms for the synthesis of state-feedback controllers with partial observation of infinite state discrete event systems modelled by Symbolic Transition Systems. We provide models of safe memoryless controllers both for potentially deadlocking and deadlock free controlled systems. The termination of the algorithms solving these problems is ensured using abstract interpretation techniques which provide an overapproximation of the transitions to disable. We then extend our algorithms to controllers with memory and to online controllers. We also propose improvements in the synthesis of controllers in the finite case which, to our knowledge, provide more permissive solutions than what was previously proposed in the literature. Our tool SMACS gives an empirical validation of our methods by showing their feasibility, usability and efficiency.

Deadlock-free discrete controller synthesis for infinite state systems

“…The controller synthesis of infinite state systems modeled by Petri Nets has also been considered by Holloway et al [8]. Regarding models more closely related to our ASTSs, one can find the work of Le Gall et al [9] that control symbolic transition systems with variables as well as Kalyon et al [10], in an asynchronous framework and with finite alphabets.…”

Discrete Controller Synthesis for Infinite State Systems with ReaX

“…We shortly introduce in this section the model of Arithmetic Symbolic Transition Systems allowing to model reactive systems handling data (a mix between the STS introduced by Kalyon et al (2011) and the Boolean system of ). We further formally present the invariance control problem and our algorithms within this framework.…”

“…Note that if the uncontrollable variables are Boolean variables as well and if only one of the input variables can be true at each instant, then we obtain a finite set of actions some of them being controllable and the other ones uncontrollable, as in the classical Ramadge & Wonham framework. In that case, and if applied to a system with distinct locations as explained in Remark 4, then our methodology is reduced to the one of Kalyon et al (2011) and implemented in Smacs 3 when all state variables are fully observable.…”

“…The controller synthesis of infinite state systems modeled by Petri Nets has also been considered by Holloway et al (1997). The control of symbolic transition systems with variables has also been studied by Le Gall et al (2005) and Kalyon et al (2011) in an asynchronous framework and with finite alphabets.…”

“…As variables in infinite domains are manipulated, these algorithms are based on interpretation techniques that overapproximate the state space that has to be forbidden by control, hence performs the computation on an abstract (infinite) domain. Our technique is similar to the one of Le Gall et al (2005) and Kalyon et al (2011), who consider the control of automata with internal variables, but with a finite alphabet of actions 2 . We present the ASTS model and our algorithms in Section 2.…”