Switched Systems with Transient Unsustainable Modes

Ensuring constraint satisfaction is distinctly challenging for externally switched systems. Previous work addressing these challenges has focused on cases where the time between switches is longer than some minimum dwell time. While this admits assurances of feasibility, it precludes uncontrollable modes. Further, the presence of poorly behaved modes, where the control actions only narrowly overcome instability, can greatly decrease the size of the switched system’s persistently feasible regions. To surmount these issues, this work examines systems with transient modes that will only be active for some maximum dwell time. Corresponding feasible regions, represented by safe-sets are developed that make use of these transient modes. Not only does this permit feasibility assurances in systems with uncontrollable modes, but this also limits the impact poorly behaving modes. These benefits are demonstrated in two numerical examples. Further, the implementation of these results in model predictive control is discussed.