9 research outputs found
Timed Parity Games: Complexity and Robustness
We consider two-player games played in real time on game structures with
clocks where the objectives of players are described using parity conditions.
The games are \emph{concurrent} in that at each turn, both players
independently propose a time delay and an action, and the action with the
shorter delay is chosen. To prevent a player from winning by blocking time, we
restrict each player to play strategies that ensure that the player cannot be
responsible for causing a zeno run. First, we present an efficient reduction of
these games to \emph{turn-based} (i.e., not concurrent) \emph{finite-state}
(i.e., untimed) parity games. Our reduction improves the best known complexity
for solving timed parity games. Moreover, the rich class of algorithms for
classical parity games can now be applied to timed parity games. The states of
the resulting game are based on clock regions of the original game, and the
state space of the finite game is linear in the size of the region graph.
Second, we consider two restricted classes of strategies for the player that
represents the controller in a real-time synthesis problem, namely,
\emph{limit-robust} and \emph{bounded-robust} winning strategies. Using a
limit-robust winning strategy, the controller cannot choose an exact
real-valued time delay but must allow for some nonzero jitter in each of its
actions. If there is a given lower bound on the jitter, then the strategy is
bounded-robust winning. We show that exact strategies are more powerful than
limit-robust strategies, which are more powerful than bounded-robust winning
strategies for any bound. For both kinds of robust strategies, we present
efficient reductions to standard timed automaton games. These reductions
provide algorithms for the synthesis of robust real-time controllers
Strategic (Timed) Computation Tree Logic
We define extensions of CTL and TCTL with strategic operators, called
Strategic CTL (SCTL) and Strategic TCTL (STCTL), respectively. For each of the
above logics we give a synchronous and asynchronous semantics, i.e., STCTL is
interpreted over networks of extended Timed Automata (TA) that either make
synchronous moves or synchronise via joint actions. We consider several
semantics regarding information: imperfect (i) and perfect (I), and recall:
imperfect (r) and perfect (R). We prove that SCTL is more expressive than ATL
for all semantics, and this holds for the timed versions as well. Moreover, the
model checking problem for SCTL[ir] is of the same complexity as for ATL[ir],
the model checking problem for STCTL[ir] is of the same complexity as for TCTL,
while for STCTL[iR] it is undecidable as for ATL[iR]. The above results suggest
to use SCTL[ir] and STCTL[ir] in practical applications. Therefore, we use the
tool IMITATOR to support model checking of STCTL[ir]
Linear Time Logic Control of Discrete-Time Linear Systems
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
Commande d'une classe de systèmes hybrides par automates hybrides rectangulaires
Notre travail de recherche concerne l étude de la commande à base de modèles pour une sous-classe de systèmes dynamiques hybrides (SDH). L outil de modélisation choisi est l automate hybride rectangulaire (AHR) pour sa puissance d analyse. Nous proposons ainsi une méthode pour la synthèse de la commande des SDH modélisés par des AHR. Cette méthode repose sur l application d une procédure amont/aval de commande hors-ligne qui détermine d une façon maximale permissive les nouvelles gardes de transition de l automate respectant des spécifications de commande imposées par l utilisateur. Tous les calculs réalisés reposent sur la détermination de la durée de séjour, valeur contrainte par l espace atteignable du sommet correspondant. La garde portant à la fois sur l état continu et sur l événement discret, la commande se fait par ce dernier car il s agit du seul élément contrôlable. Nous nous intéressons alors à la construction du contrôleur temporisé autorisant l occurrence des événements contrôlables du système dans un intervalle d horloge défini au sens de la maximale permissivité.In this thesis, we study the control of a class of hybrid dynamic systems (HDS). The chosen modeling tool is the rectangular hybrid automaton (RHA) for his analysis power. We propose a method for the control synthesis of HDS modeled with RHA. This method consists on the application of a downstream/upstream offline control procedure that determines in a maximal permissive way the new automaton transition guards respecting the desired control specifications. All computations are based on the determination of the duration of stay, a value constrained by the reachable space of the corresponding location. Since the guard refers to both continuous state and discrete event, the control is made by the latter because it is the controllable element. Then we are interested in the construction of the timed controller authorizing the system controllable event occurrence in a clock interval defined in a maximal permissive way.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF
Dense Real-time Games
The rapid development of complex and safety-critical systems requires the use of reliable verification methods and tools for system design (synthesis). Many systems of interest are reactive, in the sense that their behavior depends on the interaction with the environment. A natural framework to model them is a two-player game: the system versus the environment. In this context, the central problem is to determine the existence of a winning strategy according to a given winning condition. We focus on real-time systems, and choose to model the related game as a nondeterministic timed automaton. We express winning conditions by formulas of the branching-time temporal logic TCTL. While timed games have been studied in the literature, timed games with dense-time winning conditions constitute a new research topic. The main result of this paper is an exponential-time algorithm to check for the existence of a winning strategy for TCTL games where equality is not allowed in the timing constraints. Our approach consists on translating to timed tree automata both the game graph and the winning condition, thus reducing the considered decision problem to the emptiness problem for this class of automata. The proposed algorithm matches the known lower bound on timed games. Moreover, if we relax the limitation we have placed on the timing constraints, the problem becomes undecidable