Safe & robust reachability analysis of hybrid systems

Hybrid systems—more precisely, their mathematical models—can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability—namely, the reflexive and transitive closure of a transition relation—can be unsafe, i.e., it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states. Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust w.r.t. small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exemplify the gap between the set of reachable states and the supersets computed by safe reachability and its best robust approximation

On bicontinuous bisimulation and the preservation of stability

Since Pappas et all. transferred the notion of bisimulation from computer science to control theory, it has attracted quite some attention in the hybrid systems community[1]. Notably, bisimulation relations are used to reduce the complexity of dynamic systems, while preserving reachability notions [1]. In [2], we argued that bisimulation needs to be strengthened with continuity conditions, in order to preserve other control science notions as well. This idea was independently explored in [3,4,5] where modal and temporal logics are extended with topological operators, to be able to reason about robustness of a control strategy for embedded systems

On bicontinuous bisimulation and the preservation of stability

Since Pappas et all. transferred the notion of bisimulation from computer science to control theory, it has attracted quite some attention in the hybrid systems community[1]. Notably, bisimulation relations are used to reduce the complexity of dynamic systems, while preserving reachability notions [1]. In [2], we argued that bisimulation needs to be strengthened with continuity conditions, in order to preserve other control science notions as well. This idea was independently explored in [3,4,5] where modal and temporal logics are extended with topological operators, to be able to reason about robustness of a control strategy for embedded systems