1998
DOI: 10.1109/9.664153
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Hierarchical hybrid control systems: a lattice theoretic formulation

Abstract: The notion of dynamical consistency [12], [6] is extended to hybrid systems so as to define the set of dynamically consistent hybrid partition machines associated with a continuous system S. Following the formulation of the notions of betweenblock and in-block controllable hybrid partition machines, the lattice HIBC(S) of hybrid in-block controllable partition machines is defined and investigated. Based on these constructions, the definition and properties of hierarchical-hybrid control systems are presented t… Show more

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Cited by 105 publications
(65 citation statements)
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“…Finally, we would like to emphasize that the idea of using symbolic models for the control of continuous systems is not new and motivated much research in the area of hybrid systems [4], [12], [14], [24], [29], [32], [34], [40], [42], [47], [54]. Even though the use of symbolic models was advocated by these and many other researchers, the applicability of the proposed methods has always remained an open problem due to the lack of results ensuring existence of symbolic models for control systems.…”
Section: Related Workmentioning
confidence: 99%
“…Finally, we would like to emphasize that the idea of using symbolic models for the control of continuous systems is not new and motivated much research in the area of hybrid systems [4], [12], [14], [24], [29], [32], [34], [40], [42], [47], [54]. Even though the use of symbolic models was advocated by these and many other researchers, the applicability of the proposed methods has always remained an open problem due to the lack of results ensuring existence of symbolic models for control systems.…”
Section: Related Workmentioning
confidence: 99%
“…Proof: The result follows by differentiating both sides of (10) with respect to time and noting that . Note that the switching function dynamics characterized by (14) defines a fixed-order dynamic compensator of the form given by (8), (9). Specifically, defining the compensator state as so that , the dynamic compensator structure is given by (15) (16) Now, it follows from Theorems 5.3 and 6.1 that for all the nonlinear feedback controlled dynamical system given by (1), (15), and (16), drives to in a finite time .…”
Section: Extensions To Nonlinear Dynamic Compensationmentioning
confidence: 99%
“…Abstraction is a key concept for providing ways to connect disjointed worlds together. In [4,5], the notions of abstraction, or aggregation, refer to grouping the system states into equivalence classes. Depending on the cardinality of the resulting quotient space, there may be discrete or continuous abstractions.…”
Section: Hierarchical Architecture For Multi-vehicle Multi-modal Systemsmentioning
confidence: 99%