Stratified ODEs and Necessary Conditions For Robustness

Cristopher Hermosilla*

We study a special class of discontinuous differential equation where the singularities have a stratified structure. Particularly, we study some notions of robustness of the solutions and we give some condition to obtain it. This type of equation appears when considering Optimal Control or Stabilization problems with or without state-constraints for classical or discontinuous dynamics, more precisely, it appears in the feedback synthesis from the value function. The main motivation for introducing this type of ODEs relies in some recents work about optimal control problems with state-constraint domain that admits from the very beginning a stratified decomposition.

Mathematics Subject Classification: 34A36 58A35 93D09

Keywords: Discontinuous ODEs; Stratified systems; Stabilization; Robustness

Minisymposion: On Optimal Feedback Control for Partial Differential Equations: Theory and Numerical Methods