Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint propagation techniques

Nacim Ramdani (1) , Nedialko S. Nedialkov (2)

1 IDH - Interactive Digital Humans
2 McMaster University - Department of Computing and Software

We investigate solution techniques for numerical constraint satisfaction problems and vali- dated numerical set integration methods for computing reachable sets of nonlinear hybrid dynamical systems in presence of uncertainty. To use interval simulation tools with higher dimensional hybrid systems, while assuming large domains for either initial continuous state or model parameter vectors, we need to solve the problem of flow/sets intersection in an effective and reliable way. The main idea developed in this paper is first to derive an ana- lytical expression for the boundaries of continuous flows, using interval Taylor methods and techniques for controlling the wrapping effect. Then, the event detection and localization problems underlying flow/sets intersection are expressed as numerical constraint satisfaction problems, which are solved using global search methods based on branch-and-prune algo- rithms, interval analysis and consistency techniques. The method is illustrated with hybrid systems with uncertain nonlinear continuous dynamics and nonlinear invariants and guards.

Domaines: Automatique; Intelligence artificielle [cs.AI]

Nacim Ramdani, Nedialko S. Nedialkov. Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint propagation techniques. Nonlinear Analysis: Hybrid Systems, 2011, 5 (2), pp.149-162. ⟨10.1016/j.nahs.2010.05.010⟩. ⟨hal-00611996⟩