Detection of different type events in hybrid dynamical systems

Abstract

Hybrid dynamical or simply hybrid systems (HS) are a modern apparatus for modeling discrete-continuous processes in different applications such as power engineering, aeronautics, manufacturing, economics, transport dispatching, etc. The key difference of HSs from classical dynamic systems is the presence of continuous mode switching events. Event times are defined by the zeroes of continuous event functions. If it is impossible to symbolically compute an event time. To do it one uses an event detection algorithm working together with a differential equation integration algorithm. Events in HSs are traditionally divided into state events and time events. Only explicit time events with event functions in the form of linear polynomials in time are usually considered in the literature. This paper addresses the class of implicit time events and lists their possible sources. Moreover, the traditional classification of events into unilateral, bilateral and accuracy critical events is expanded by adding difficult-to-detect events. These events are characterized by event functions crossing zero several times within one integration step. Not all algorithms can guarantee detecting events of this type. Heterogeneous HSs including processes of different physical nature are in general characterized by significantly stiff and high-dimensional modes usually defined in a form of differential-algebraic systems of equations with events of different types. The last feature limits the application of classical event detection algorithms oriented to a single event type. That is why the paper proposes the methodology of complex event detection consisting in using separate event detection algorithm for each event type. The joint work of several algorithms can ensure correct detection of events of different types and also may improve the efficiency. A complex event detection algorithm guaranteeing detection of all events is constructed for a particular HS. The complex algorithm demonstrates an average speed up of 17%.