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Towards a geometric theory of hybrid systems
 In HSCC’00, number 1790 in LNCS
, 2000
"... Abstract. We propose a framework for a geometric theory of hybrid systems. Given a deterministic, nonblocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non ..."
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Cited by 55 (18 self)
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Abstract. We propose a framework for a geometric theory of hybrid systems. Given a deterministic, nonblocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally nonsmooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.
Modular specifications of hybrid systems in CHARON
 IN CHARON. INHYBRID SYSTEMS: COMPUTATION AND CONTROL, THIRD INTERNATIONAL WORKSHOP, VOLUME LNCS 1790
, 2000
"... We propose a language, called Charon, for modular specification of interacting hybrid systems. For hierarchical description of the system architecture, Charon supports building complex agents via the operations of instantiation, hiding, and parallel composition. For hierarchical description of the ..."
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Cited by 53 (12 self)
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We propose a language, called Charon, for modular specification of interacting hybrid systems. For hierarchical description of the system architecture, Charon supports building complex agents via the operations of instantiation, hiding, and parallel composition. For hierarchical description of the behavior of atomic components, Charon supports building complex modes via the operations of instantiation, scoping, and encapsulation. Features such asweak preemption, history retention, and externally defined Java functions, facilitate the description of complex discrete behavior. Continuous behavior can be specified using differential as well as algebraic constraints, and invariants restricting the ow spaces, all of which can be declared at various levels of the hierarchy. The modular structure of the language is not merely syntactic, but can be exploited during analysis. We illustrate this aspect by presenting a scheme for modular simulation in which each mode can be compiled solely based on the locally declared information to execute its discrete and continuous updates, and furthermore, submodes can integrate at a finer time scale than the enclosing modes.
Compositional refinement for hierarchical hybrid systems
, 2001
"... In this paper, we develop a theory of modular design and refinement of hierarchical hybrid systems. In particular, we present compositional tracebased semantics for the language Charon that allows modular specification of interacting hybrid systems. For hierarchical description of the system archi ..."
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Cited by 47 (16 self)
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In this paper, we develop a theory of modular design and refinement of hierarchical hybrid systems. In particular, we present compositional tracebased semantics for the language Charon that allows modular specification of interacting hybrid systems. For hierarchical description of the system architecture, Charon supports building complex agents via the operations of instantiation, hiding, and parallel composition. For hierarchical description of the behavior of atomic components, Charon supports building complex modes via the operations of instantiation, scoping, and encapsulation. We develop an observational trace semantics for agents as well as for modes, and define a notion of refinement for both, based on trace inclusion. We show this semantics to be compositional with respect to the constructs in the language. 1 Introduction Modern software design paradigms promote hierarchy as one of the key constructs for structuring complex specifications. We are concerned with two distinct notions of hierarchy. In architectural hierarchy, a system with a collection of communicating agents is constructed by parallel composition of atomic agents, and in behavioral hierarchy, the behavior of an individual agent is described by hierarchical sequential composition. The former hierarchy is present in almost all concurrency formalisms, and the latter, while present in all blockstructured programming languages, was introduced for statemachinebased modeling in Statecharts [9], and forms an integral part of modern notations such as UML [5].
Masaccio: A formal model for embedded components
 IN PROC. FIRST IFIP INTERNATIONAL CONFERENCE ON THEORETICAL COMPUTER SCIENCE, LNCS 1872
, 2000
"... Masaccio is a formal model for hybrid dynamical systems which are built from atomic discrete components (difference equations) and atomic continuous components (differential equations) by parallel and serial composition, arbitrarily nested. Each system component consists of an interface, which det ..."
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Cited by 42 (5 self)
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Masaccio is a formal model for hybrid dynamical systems which are built from atomic discrete components (difference equations) and atomic continuous components (differential equations) by parallel and serial composition, arbitrarily nested. Each system component consists of an interface, which determines the possible ways of using the component, and a set of executions, which de ne the possible behaviors of the component in real time.
Rectangular Hybrid Games
 In CONCUR 99, LNCS 1664
, 1999
"... In order to study control problems for hybrid systems, we generalize hybrid automata to hybrid games  say, controller vs. plant. If we specify the continuous dynamics by constant lower and upper bounds, we obtain rectangular games. We show that for rectangular games with objectives expressed in Lt ..."
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Cited by 40 (4 self)
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In order to study control problems for hybrid systems, we generalize hybrid automata to hybrid games  say, controller vs. plant. If we specify the continuous dynamics by constant lower and upper bounds, we obtain rectangular games. We show that for rectangular games with objectives expressed in Ltl (linear temporal logic), the winning states for each player can be computed, and winning strategies can be synthesized. Our result is sharp, as already reachability is undecidable for generalizations of rectangular systems, and optimal  singly exponential in the size of the game structure and doubly exponential in the size of the Ltl objective. Our proof systematically generalizes the theory of hybrid systems from automata (singleplayer structures) [9] to games (multiplayer structures): we show that the successively more general infinitestate classes of timed, 2d rectangular, and rectangular games induce successively weaker, but still finite, quotient structures called game bisimilarity, game similarity, and game trace equivalence. These quotients can be used, in particular, to solve the Ltl control problem.
A modular visual model for hybrid systems
 FORMAL TECHNIQUES IN REALTIME AND FAULTTOLERANT SYSTEMS
, 1998
"... Visual description techniques are particularly important for the design of hybrid systems because specifications of such systems must usually be discussed between engineers from a number of different disciplines. Modularity is vital for hybrid systems not only because it allows to handle large syste ..."
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Cited by 35 (16 self)
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Visual description techniques are particularly important for the design of hybrid systems because specifications of such systems must usually be discussed between engineers from a number of different disciplines. Modularity is vital for hybrid systems not only because it allows to handle large systems, but also because hybrid systems are naturally decomposed into the system itself and its environment. Based on two different interpretations for hierarchic graphs and on a clear hybrid computation model, we develop HyCharts, two modular visual formalisms for the specification of the architecture and behavior of hybrid systems. The operators on hierarchic graphs enable us to give a surprisingly simple denotational semantics for many concepts known from statechartlike formalisms. Due to a verygeneral composition operator, HyCharts can easily be composed with description techniques from other engineering disciplines. Such heterogeneous system specifications seem to be particularly appropriate for hybrid systems because of their interdisciplinary character.
Formal verification of hybrid systems
, 2011
"... In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines th ..."
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Cited by 34 (0 self)
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In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines the traditional statemachine based models for discrete control with classical differentialequations based models for continuously evolving physical activities. In this article, we briefly review selected existing approaches to formal verification of hybrid systems, along with directions for future research.
Deductive verification of realtime systems using STeP
 COMPUTER SCIENCE DEPARTMENT, STANFORD UNIVERSITY
, 1998
"... We present a modular framework for proving temporal properties of realtime systems, based on clocked transition systems and lineartime temporal logic. We show how deductive verification rules, verification diagrams, and automatic invariant generation can be used to establish properties of realtim ..."
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Cited by 34 (8 self)
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We present a modular framework for proving temporal properties of realtime systems, based on clocked transition systems and lineartime temporal logic. We show how deductive verification rules, verification diagrams, and automatic invariant generation can be used to establish properties of realtime systems in this framework. We also discuss global and modular proofs of the branchingtime property of nonZenoness. As an example, we present the mechanical verification of the generalized railroad crossing case study using the Stanford Temporal Prover, STeP.
Assumeguarantee reasoning for hierarchical hybrid systems
 In: HSCC. Volume 2034 of LNCS
, 2001
"... www.eecs.berkeley.edu/~{tah,marius,vinayak} Abstract. The assumeguarantee paradigm is a powerful divideandconquer mechanism for decomposing a verification task about a system into subtasks about the individual components of the system. The key to assumeguarantee reasoning is to consider each comp ..."
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Cited by 31 (1 self)
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www.eecs.berkeley.edu/~{tah,marius,vinayak} Abstract. The assumeguarantee paradigm is a powerful divideandconquer mechanism for decomposing a verification task about a system into subtasks about the individual components of the system. The key to assumeguarantee reasoning is to consider each component not in isolation, but in conjunction with assumptions about the context of the component. Assumeguarantee principles are known for purely concurrent contexts, which constrain the input data of a component, as well as for purely sequential contexts, which constrain the entry configurations of a component. We present a model for hierarchical system design which permits the arbitrary nesting of parallel as well as serial composition, and which supports an assumeguarantee principle for mixed parallelserial contexts. Our model also supports both discrete and continuous processes, and is therefore wellsuited for the modeling and analysis of embedded software systems which interact with realworld environments. Using an example of two cooperating robots, we show refinement between a highlevel model which specifies continuous timing constraints and an implementation which relies on discrete sampling. 1
Hybrid I/O Automata Revisited
 Proceedings Fourth International Workshop on Hybrid Systems: Computation and Control (HSCC'01
, 2001
"... In earlier work, we developed a mathematical hybrid I/O automaton (HIOA) modeling... ..."
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Cited by 28 (3 self)
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In earlier work, we developed a mathematical hybrid I/O automaton (HIOA) modeling...