Conference article

Rigorous simulation of hybrid systems relies critically on having a semantics that constructs enclosures. Edalat and Pattinson’s work on the domain-theoretic semantics of hybrid systems almost provides what is needed; with two exceptions. First; domain-theoretic methods leave many operational concerns implicit. As a result; the feasibility of practical implementations is not obvious. For example; their semantics appears to rely on repeated interval splitting for state space variables. This can lead to exponential blow up in the cost of the computation. Second; common and even simple hybrid systems exhibit Zeno behaviors. Such behaviors are a practical impediment because they make simulators loop indefinitely. This is in part due to the fact that existing semantics for hybrid systems generally assume that the system is non-Zeno. The feasibility of reasonable implementations is addressed by specifying the semantics algorithmically. We observe that the amount of interval splitting can be influenced by the representation of function enclosures. Parameterizing the semantics with respect to enclosure representation provides a precise specification of the functionality needed from them; and facilitates studying their performance characteristics. For example; we find that non-constant enclosure representations can alleviate the need for interval splitting on dependent variables. We address the feasibility of dealing with Zeno systems by taking a fresh look at event detection and localization. The key insight is that computing enclosures for hybrid behaviors over intervals containing multiple events does not necessarily require separating these events in time; even when the number of events is unbounded. In contrast to current methods for dealing with Zeno behaviors; this semantics does not require reformulating the hybrid system model specifically to enable a transition to a post-Zeno state. The new semantics does not sacrifice the key qualities of the original work; namely; convergence on separable systems.

hybrid systems semantics; hybrid systems implementation; Zeno behavior; event localization