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140
Effective Synthesis of Switching Controllers for Linear Systems
, 2000
"... In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the sys ..."
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Cited by 110 (8 self)
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In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the system from one "mode" to another in order to avoid a set of bad states, and propose an abstract algorithm which solves the problem by an iterative computation of reachable states. We have implemented a concrete version of the algorithm, which uses a new approximation scheme for reachability analysis of linear systems.
Approximation metrics for discrete and continuous systems
 IEEE Transactions on Automatic Control
, 2005
"... Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In thi ..."
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Cited by 105 (16 self)
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Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In this paper, we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion, approximate simulation, and approximate bisimulation relations. We define a hierarchy of approximation pseudometrics between two systems that quantify the quality of the approximation, and capture the established exact relationships as zero sections. Our approximation framework is compositional for a synchronous composition operator. Algorithms are developed for computing the proposed pseudometrics, both exactly and approximately. The exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations, or dually, the solution of a static game whose cost is the socalled branching distance between the systems. Approximations for the pseudometrics can be obtained by considering Lyapunovlike functions called simulation and bisimulation functions. We illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems.
Reachability of uncertain linear systems using zonotopes
 IN HYBRID SYSTEMS : COMPUTATION AND CONTROL, LNCS 3414
, 2005
"... We present a method for the computation of reachable sets of uncertain linear systems. The main innovation of the method consists in the use of zonotopes for reachable set representation. Zonotopes are special polytopes with several interesting properties: they can be encoded efficiently, they are ..."
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Cited by 97 (14 self)
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We present a method for the computation of reachable sets of uncertain linear systems. The main innovation of the method consists in the use of zonotopes for reachable set representation. Zonotopes are special polytopes with several interesting properties: they can be encoded efficiently, they are closed under linear transformations and Minkowski sum. The resulting method has been used to treat several examples and has shown great performances for high dimensional systems. An extension of the method for the verification of piecewise linear hybrid systems is proposed.
Spaceex: Scalable verification of hybrid systems
 In Proceedings of the International Conference on Computer Aided Verification
, 2011
"... Abstract. We present a scalable reachability algorithm for hybrid systems with piecewise affine, nondeterministic dynamics. It combines polyhedra and support function representations of continuous sets to compute an overapproximation of the reachable states. The algorithm improves over previous wo ..."
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Cited by 88 (5 self)
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Abstract. We present a scalable reachability algorithm for hybrid systems with piecewise affine, nondeterministic dynamics. It combines polyhedra and support function representations of continuous sets to compute an overapproximation of the reachable states. The algorithm improves over previous work by using variable time steps to guarantee a given local error bound. In addition, we propose an improved approximation model, which drastically improves the accuracy of the algorithm. The algorithm is implemented as part of SpaceEx, a new verification platform for hybrid systems, available at spaceex.imag.fr. Experimental results of full fixedpoint computations with hybrid systems with more than 100 variables illustrate the scalability of the approach. 1
Hierarchical Modeling and Analysis of Embedded Systems
, 2003
"... This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is ..."
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Cited by 78 (24 self)
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This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in the design of embedded control software using examples from automated highways concerning vehicle coordination
Computational techniques for the verification of hybrid systems
 Proceedings of the IEEE
, 2003
"... Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous sta ..."
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Cited by 72 (9 self)
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Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous state dynamics, represented by differential equations. The embedded autopilot of a modern commercial jet is a prime example of a hybrid system: the autopilot modes correspond to the application of different control laws, and the logic of mode switching is determined by the continuous state dynamics of the aircraft, as well as through interaction with the pilot. To understand the behavior of hybrid systems, to simulate, and to control these systems, theoretical advances, analyses, and numerical tools are needed. In this paper, we first present a general model for a hybrid system along with an overview of methods for verifying continuous and hybrid systems. We describe a particular verification
Reachability Analysis of Hybrid Systems via Predicate Abstraction
 Hybrid Systems: Computation and Control, Fifth International Workshop, LNCS 2289
, 2002
"... Predicate abstraction has emerged to be a powerful technique for extracting finitestate models from infinitestate discrete programs. This paper presents algorithms and tools for reachability analysis of hybrid systems by combining the notion of predicate abstraction with recent techniques for appr ..."
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Cited by 62 (8 self)
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Predicate abstraction has emerged to be a powerful technique for extracting finitestate models from infinitestate discrete programs. This paper presents algorithms and tools for reachability analysis of hybrid systems by combining the notion of predicate abstraction with recent techniques for approximating the set of reachable states of linear systems using polyhedra. Given a hybrid system and a set of userdefined predicates, we consider the finite discrete quotient whose states correspond to all possible truth assignments to the input predicates. The tool performs an onthefly exploration of the abstract system by using weakest preconditions to compute abstract transitions corresponding to the discrete switches and conservative polyhedral approximations to compute abstract transitions corresponding to continuous flows. Compared to tools such as Checkmate and d/dt, this approach requires significantly less computational resources as the emphasis is shifted from computing the reachable set to searching in the abstract quotient. We demonstrate the feasibility of the proposed technique by analyzing a parametric timingbased mutual exclusion protocol and safety of a simple controller for vehicle coordination.
A control problem for affine dynamical systems on a fulldimensional polytope
 AUTOMATICA
, 2004
"... ..."
Abstraction and CounterexampleGuided Refinement in Model Checking of Hybrid Systems
, 2003
"... Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finitestate abstraction. Model checking can be inconclusive, however, in which case t ..."
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Cited by 55 (7 self)
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Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finitestate abstraction. Model checking can be inconclusive, however, in which case the abstraction must be refined. This paper presents a new procedure to perform this refinement operation for abstractions of hybrid systems. Following an approach originally developed for finitestate systems [11, 25], the refinement procedure constructs a new abstraction that eliminates a counterexample generated by the model checker. For hybrid systems, analysis of the counterexample requires the computation of sets of reachable states in the continuous state space. We show how such reachability computations with varying degrees of complexity can be used to refine hybrid system abstractions efficiently.
Impulse differential inclusions: A viability approach to hybrid systems
 IEEE Transactions on Automatic Control
, 2002
"... Abstract. Impulse differential inclusions are introduced as a framework for modelling hybrid phenomena. Connections to standard problems in area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an i ..."
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Cited by 49 (7 self)
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Abstract. Impulse differential inclusions are introduced as a framework for modelling hybrid phenomena. Connections to standard problems in area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these conditions, methods are developed for approximating their viability and invariance kernels, that is the largest subset that is viable or invariant under the action of the impulse differential inclusion. The results are demonstrated on examples. 1.