Limit occupational measures set for a control system and averaging of singularity perturbed control systems
This paper investigates the asymptotic behaviour of the so-called occupational probability \[ {1\over s}\lambda \biggl\{ \tau\in [0,S]/ \bigl(y(\tau), u(\tau)\bigr) \in Q\biggr\} \] where \(Q\) is a given set and \((y, u)\) are associated with a control system \[ y'(\tau)= g\bigl(y (\tau),u(\tau) \bigr) \quad \tau\in [0,S]. \] The existence of a limit of such an occupational measure when \(s\to+\infty\) is given. For a singular perturbation control problem, the authors prove that the slow variables can be approached by solutions to a differential inclusion obtained through the limit of suitable occupational measures.
scientific article; zbMATH DE number 1295256
scientific article