Robust Controller Synthesis in Timed Büchi Automata: A Symbolic Approach

Abstract

We solve in a purely symbolic way the robust controller synthesis problem in timed automata with Büchi acceptance conditions. The goal of the controller is to play according to an accepting lasso of the automaton, while resisting to timing perturbations chosen by a competing environment. The problem was previously shown to be PSPACEcomplete using regions-based techniques, but we provide a first tool solving the problem using zones only, thus more resilient to state-space explosion problem. The key ingredient is the introduction of branching constraint graphs allowing to decide in polynomial time whether a given lasso is robust, and even compute the largest admissible perturbation if it is. We also make an original use of constraint graphs in this context in order to test the inclusion of timed reachability relations, crucial for the termination criterion of our algorithm. Our techniques are illustrated using a case study on the regulation of a train network. This work was funded by ANR project Ticktac (ANR-18-CE40-0015).

Computing maximally-permissive strategies in acyclic timed automata

“…We were unable to prove our intuition that there is no reason for the player to iterate a cycle. Following [BGMRS19], we might first consider fixing a timed automaton made of a single cycle, study how permissiveness evolves along one run in this cycle, and compute the optimal permissiveness for being able to take a cycle forever. Exploiting 2-Lipschitz continuity of the permissiveness function, we could also develop approximating techniques, both for making our computations more efficient in the acyclic case and to handle cycles.…”

“…Finally, and perhaps more importantly, our setting is quite close to that of [BMS15], but with a more quantitative focus: we aim at computing the optimal permissiveness for all winning configurations (with reachability objective), while only a global lower bound (of the form 1/m where m is doubly-exponential in the size of the input) is obtained in [BMS15]. Similar results to those of [BMS15] are obtained in [SBMR13,BGMRS19] for Büchi objectives; such extensions are part of our future work.…”

Parametric updates in parametric timed automata

“…Our construction is reminiscent of the parametric difference bound matrices (PDBMs) defined in [QSW17, section III.C] where the author revisit the result of the binary reachability relation over both locations and clock valuations in TAs; however, parameters of [QSW17] are used to bound in time a run that reaches a given location, while we use parameters directly in guards and resets along the run, which make them active components of the run specifically for intersection with parametric guards, key point not tackled in [QSW17]. Related DBMs with an additional parameter are studied such as shrunk DBMs [SBM14;Bus+19] and infinitesimally enlarged DBMs [San15].…”