• DOI:10.1007/3-540-64358-3_43
• Corpus ID: 37953001

Hierarchical Hybrid Systems: Partition Deformations and Applications to the Acrobot System

@inproceedings{Lemch1998HierarchicalHS,
  title={Hierarchical Hybrid Systems: Partition Deformations and Applications to the Acrobot System},
  author={Ekaterina S. Lemch and Peter E. Caines},
  booktitle={HSCC},
  year={1998}
}

• E. S. Lemch, P. Caines
• Published in HSCC 13 April 1998
• Mathematics

In [3],[5] the notion of dynamical consistency was formulated for hybrid systems so as to define the set of dynamically consistent hybrid partition machines Mπ, π e П, associated with a given continuous system S. This theory includes the notions of a hybrid between-block (HBBC) and in-block controllable (HIBC) partition machine, the lattice HIBC(S) of (HIBC) partition machines, and that of the associated hierarchical-hybrid feedback control systems. In this paper, a brief summary of this theory is presented, and the robustness properties of a partition machine Mπ with respect to deformations of the boundaries of the blocks of π is outlined. An application to the hybrid control of an underactuated double pendulum (Acrobot) system and a fully actuated double pendulum system is then presented. The pendulum example also introduces some properties of the blocks of a state space partition (such as in-block controllability to a distinguished state and controlled umbilical paths) which promise to facilitate the design of hierarchical hybrid control systems. Finally, some global controllability results for nonlinear systems are sketched which have application to the construction of HIBC partitions for mechanical systems.