Journal Article

Partition deformations in hierarchical hybrid control systems

Ekaterina S. Lemch and Peter E. Caines

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 18, issue 4, pages 531-557
Published in print December 2001 | ISSN: 0265-0754
Published online December 2001 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/18.4.531
Partition deformations in hierarchical hybrid control systems

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Hierarchical hybrid control (HHC) (Caines & Wei, submitted) needs to be applicable to systems in which the dynamics of the system, the nature of the controllable flows, and the positions of the boundaries of any partition can only be approximately specified. In this paper, conditions are given under which the dynamics of a high‐level HHC system Mπ, and its associated set of control laws, are robust (that is to say, insensitive) with respect to small perturbations of the partitions defining Mπ and small perturbations of the controllable flow. This analysis employs two notions of the deformation of a partition π specified respectively by (i) maps of the boundaries and (ii) maps of the blocks of π. Further, the robustness properties of the partition machine Mπ are investigated for deformations of the controllable flow and, finally, for certain mechanical systems.

Keywords: hierarchical hybrid control; partitions; partition deformations; Hamiltonian control systems

Journal Article.  0 words. 

Subjects: Mathematics

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