BMMS are hybrid systems that switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent rates that vary within given bounded sets. The scheduler repeatedly proposes a time and a mode while the environment chooses an allowable rate for that mode; the state of the system changes linearly in the direction of the rate. The scheduler aims to keep the state within a safe set, while the environment aimis to leave it. We study the problem of existence of a winning scheduler strategy, and associated complexity question
