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The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewiselinear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard programanalysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic modelchecking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.
The Theory of Hybrid Automata
, 1996
"... A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on pur ..."
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Cited by 685 (12 self)
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A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on purely discrete state spaces only. In particular, various classes of hybrid automata induce finitary trace equivalence (or similarity, or bisimilarity) relations on an uncountable state space, thus permitting the application of various modelchecking techniques that were originally developed for finitestate systems.
Alternatingtime Temporal Logic
 Journal of the ACM
, 1997
"... Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general var ..."
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Cited by 620 (53 self)
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Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general variety of temporal logic: alternatingtime temporal logic offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves. While lineartime and branchingtime logics are natural specification languages for closed systems, alternatingtime logics are natural specification languages for open systems. For example, by preceding the temporal operator "eventually" with a selective path quantifier, we can specify that in the game between the system and the environment, the system has a strategy to reach a certain state. Also the problems of receptiveness, realizability, and controllability can be formulated as modelchecking problems for alternatingtime formulas.
Conflict Resolution for Air Traffic Management: A Study in Multiagent Hybrid Systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1998
"... Air Traffic Management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system. In this p ..."
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Cited by 287 (50 self)
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Air Traffic Management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system. In this paper, we present a method to synthesize provably safe conflict resolution maneuvers. The method models the aircraft and the maneuver as a hybrid control system and calculates the maximal set of safe initial conditions for each aircraft so that separation is assured in the presence of uncertainties in the actions of the other aircraft. Examples of maneuvers using both speed and heading changes are worked out in detail.
Controllers for Reachability Specifications for Hybrid Systems
 Automatica
, 1999
"... The problem of systematically synthesizing hybrid controllers which satisfy multiple control objectives is considered. We present a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisfies the most important objective (which we ..."
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Cited by 172 (42 self)
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The problem of systematically synthesizing hybrid controllers which satisfy multiple control objectives is considered. We present a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisfies the most important objective (which we refer to as safety). The system performance with respect to lower priority objectives (which we refer to as efficiency) can then be optimized within this class. We motivate our approach by showing how the proposed synthesis technique simplifies to well known results from supervisory control and pursuit evasion games when restricted to purely discrete and purely continuous systems respectively. We then illustrate the application of this technique to two examples, one hybrid (the steam boiler benchmark problem), and one primarily continuous (a flight vehicle management system with discrete flight modes). 1 Introduction Hybrid systems, or systems that involve the interaction of discrete and co...
CONTROLLER SYNTHESIS FOR TIMED AUTOMATA
"... In this work we tackle the following problem: given a timed automaton, restrict its transition relation in a systematic way so that all the remaining behaviors satisfy certain properties. This is an extension of the problem of controller synthesis for discrete event dynamical systems, where in addi ..."
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Cited by 157 (14 self)
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In this work we tackle the following problem: given a timed automaton, restrict its transition relation in a systematic way so that all the remaining behaviors satisfy certain properties. This is an extension of the problem of controller synthesis for discrete event dynamical systems, where in addition to choosing among actions, the controller have the option of doing nothing and let the time pass. The problem is formulated using the notion of a realtime game, and a winning strategy is constructed as a fixedpoint of an operator on the space of states and clock configurations.
Logics for Hybrid Systems
 Proceedings of the IEEE
, 2000
"... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems ..."
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Cited by 137 (12 self)
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This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems
A game theoretic approach to controller design for hybrid systems
 Proceedings of the IEEE
, 2000
"... We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and t ..."
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Cited by 126 (33 self)
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We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and discrete control and disturbance parameters. We translate safety specifications into restrictions on the system’s reachable sets of states. Then, using analysis based on optimal control and game theory for automata and continuous dynamical systems, we derive Hamilton–Jacobi equations whose solutions describe the boundaries of reachable sets. These equations are the heart of our general controller synthesis technique for hybrid systems, in which we calculate feedback control laws for
Optimal Paths in Weighted Timed Automata
 HSCC
, 2001
"... We consider an optimalreachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortestpath problem for a finite directed graph. The directed gr ..."
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Cited by 124 (5 self)
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We consider an optimalreachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortestpath problem for a finite directed graph. The directed graph we construct is a refinement of the region automaton due to Alur and Dill. We present an exponential time algorithm to solve the shortestpath problem for weighted timed automata starting from a single state, and a doublyexponential time algorithm to solve this problem starting from a zone of the state space.
Games for synthesis of controllers with partial observation
 THEORETICAL COMPUTER SCIENCE
"... The synthesis of controllers for discrete event systems, as introduced by Ramadge and Wonham, amounts to computing winning strategies in parity games. We show that in this framework it is possible to extend the specifications of the supervised systems as well as the constraints on the controllers ..."
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Cited by 117 (15 self)
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The synthesis of controllers for discrete event systems, as introduced by Ramadge and Wonham, amounts to computing winning strategies in parity games. We show that in this framework it is possible to extend the specifications of the supervised systems as well as the constraints on the controllers by expressing them in the modal µcalculus. In order to express unobservability constraints, we propose an extension of the modal µcalculus in which one can specify whether an edge of a graph is a loop. This extended µcalculus still has the interesting properties of the classical one. In particular it is equivalent to automata with loop testing. The problems such as emptiness testing and elimination of alternation are solvable for such automata. The method proposed in this paper to solve a control problem consists in transforming this problem into a problem of satisfiability of a µcalculus formula so that the set of models of this formula is exactly the set of controllers that solve the problem. This transformation relies on a simple construction of the quotient of automata with loop testing by a deterministic transition system. This is enough to deal with centralized control problems. The solution of decentralized control problems uses a more involved construction of the quotient of two automata. This work extends the framework of Ramadge and Wonham in two directions. We consider infinite behaviours and arbitrary regular specifications, while the standard framework deals only with specifications on the set of finite paths of processes. We also allow dynamic changes of the set of observable and controllable events.