Time-deterministic Hybrid Transition Systems
Fifth international workshop on Hybrid Systems (HS V), Notre Dame, Indiana, September 1997, LNCS 1567, Springer Verlag, pages 238-250.
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Hybrid transition systems in their full generality describe continuous behaviour by a set of equations in each mode - an algebraic or differential equation for each state variable in terms of inputs and other state variables. Each discrete transition may be taken according to a (non-deterministic) time constraint. In this paper we restrict this model to time-deterministic discrete transitions. Thus, every transition is guarded by a condition g and has a fixed delay t. Different transitions may have different delays (including zero), but progress is enforced after the delay. Using this restriction and a composition operator which uses union of mode sets we then prove certain compositionality properties. In particular, that the parallel composition of two subsystems produces a system whose semantics is defined in terms of semantics of its constituents provided that it has a run. The restriction is well-justified in a large class of control applications where the complex mode-changing software is realised as a synchronous program.
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[N97] Simin Nadjm-Tehrani, "Time-deterministic Hybrid Transition Systems", Fifth international workshop on Hybrid Systems (HS V), Notre Dame, Indiana, September 1997, LNCS 1567, Springer Verlag, pages 238-250.