Verifying safety and persistence in hybrid systems using flowpipes and continuous invariants

We describe a method for verifying the temporal property of persistence in non-linear hybrid systems. Given some system and an initial set of states, the method establishes that system trajectories always eventually evolve into some specified target subset of the states of one of the discrete modes of the system, and always remain within this target region. The method also computes a time-bound within which the target region is always reached. The approach combines flowpipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study showing that potentially destructive stick-slip oscillations of an oil-well drill eventually die away for a certain choice of drill control parameters. The case study demonstrates how just using flowpipes or just reasoning about invariants alone can be insufficient and shows the richness of systems that one can handle with the proposed method, since the systems features modes with non-polynomial ODEs. We also propose an alternative method for proving persistence that relies solely on flowpipe computation

Operational Models for Piecewise-Smooth Systems

International audienceThis paper studies ways of constructing meaningful operational models of piecewise-smooth systems (PWS). The systems we consider are described by polynomial vector fields defined on non-overlapping semi-algebraic sets, which form a partition of the state space. Our approach is to give meaning to motion in systems of this type by automatically synthesizing operational models in the form of hybrid automata (HA). Despite appearances, it is in practice often difficult to arrive at satisfactory HA models of PWS. The different ways of building operational models that we explore in our approach can be thought of as defining different semantics for the underlying PWS. These differences have a number of interesting nuances related to phenomena such as chattering, non-determinism, so-called mythical modes and sliding behaviour