Computing reachable sets for uncertain nonlinear monotone systems

Nacim Ramdani (1, 2) , Nacim Meslem (3) , Yves Candau (4)

1 COPRIN - Constraints solving, optimization and robust interval analysis
2 IDH - Interactive Digital Humans
3 MIG - Unité Mathématique Informatique et Génome
4 CERTES EA 3481 - Centre d'Etudes et Recherches en Thermique, Environnement et Systèmes [Créteil]

We address nonlinear reachability computation for uncertain monotone systems, those for which flows preserve a suitable partial orderings on initial conditions. In a previous work Ramdani (2008), we introduced a nonlinear hybridization approach to nonlinear continuous reachability computation. By analysing the signs of off-diagonal elements of system's Jacobian matrix, a hybrid automaton can be obtained, which yields component-wise bounds for the reachable sets. One shortcoming of the method is induced by the need to use whole sets for addressing mode switching. In this paper, we improve this method and show that for the broad class of monotone dynamical systems, component-wise bounds can be obtained for the reachable set in a separate manner. As a consequence, mode switching no longer needs to use whole solution sets. We give examples which show the potentials of the new approach.

Domaines: Automatique / Robotique

Nacim Ramdani, Nacim Meslem, Yves Candau. Computing reachable sets for uncertain nonlinear monotone systems. Nonlinear Analysis: Hybrid Systems, 2010, 4 (2), pp.263-278. ⟨10.1016/j.nahs.2009.10.002⟩. ⟨hal-00629909⟩