Programming in Hybrid Constraint Languages (original) (raw)

HydLa: A High-Level Language for Hybrid Systems 1 HydLa, A Hybrid Constraint Language

We have been working on the design and implementation of HydLa, a modeling language for hybrid systems [5] 3 . The principal feature of HydLa is that it em-ploys constraint-based formalisms both in the modeling and reliable simulation of hybrid systems. We take this approach for two reasons: one is that a constraint-based formalism is non-procedural but yet provides the language with control structures including synchronization and conditionals that are expressive enough to model hybrid systems, and the other is it allows us to handle uncertainties or partial information in a smooth way. Rather few tools for hybrid systems fully exploit constraint-based formalisms. The closest previous work was Hybrid cc [2][3], but HydLa differs in that its implementation ensures the correctness of simulation results. Another constraint-based approach was CLP(F), constraint logic programming over real-valued functions [4]. Both CLP(F) and HydLa aim at rigorous simulation and handle intervals, but t...

Declarative Semantics of the Hybrid Constraint Language HydLa

ArXiv, 2019

Hybrid systems are dynamical systems with continuous evolution of states and discrete evolution of states and governing equations. We have worked on the design and implementation of HydLa, a constraint-based modeling language for hybrid systems, with a view to the proper handling of uncertainties and the integration of simulation and verification. HydLa's constraint hierarchies facilitate the description of constraints with adequate strength, but its semantical foundations are not obvious due to the interaction of various language constructs. This paper gives the declarative semantics of HydLa and discusses its properties and consequences by means of examples.

Abstractions for hybrid systems

Formal Methods in System Design, 2008

We present a procedure for constructing sound finite-state discrete abstractions of hybrid systems. This procedure uses ideas from predicate abstraction to abstract the discrete dynamics and qualitative reasoning to abstract the continuous dynamics of the hybrid system. It relies on the ability to decide satisfiability of quantifier-free formulas in some theory rich enough to encode the hybrid system. We characterize the sets of predicates that can be used to create high quality abstractions and we present new approaches to discover such useful sets of predicates. Under certain assumptions, the abstraction procedure can be applied compositionally to abstract a hybrid system described as a composition of two hybrid automata. We show that the constructed abstractions are always sound, but are relatively complete only under certain assumptions.

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 trace-based 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.