Partition deformations in hierarchical hybrid control systems

Hierarchical hybrid control (HHC) (Caines & Wei, submitted)needs to be applicable to systems in which the dynamics of thesystem, the nature of the controllable flows, and the positionsof the boundaries of any partition can only be approximatelyspecified. In this paper, conditions are given under which thedynamics of a high-level HHC system M, and its associated setof control laws, are robust (that is to say, insensitive) withrespect to small perturbations of the partitions defining Mand small perturbations of the controllable flow. This analysisemploys two notions of the deformation of a partition specifiedrespectively by (i) maps of the boundaries and (ii) maps ofthe blocks of . Further, the robustness properties of the partitionmachine M are investigated for deformations of the controllableflow and, finally, for certain mechanical systems.