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- W3169628166 endingPage "693" @default.
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- W3169628166 abstract "<p style='text-indent:20px;'>Brockett's necessary condition yields a test to determine whether a system can be made to stabilize about some operating point via continuous, purely state-dependent feedback. For many real-world systems, however, one wants to stabilize sets which are more general than a single point. One also wants to control such systems to operate safely by making obstacles and other dangerous sets repelling. <p style='text-indent:20px;'>We generalize Brockett's necessary condition to the case of stabilizing general compact subsets having a nonzero Euler characteristic in general ambient state spaces (smooth manifolds). Using this generalization, we also formulate a necessary condition for the existence of safe control laws. We illustrate the theory in concrete examples and for some general classes of systems including a broad class of nonholonomically constrained Lagrangian systems. We also show that, for the special case of stabilizing a point, the specialization of our general stabilizability test is stronger than Brockett's." @default.
- W3169628166 created "2021-06-22" @default.
- W3169628166 creator A5068996884 @default.
- W3169628166 creator A5082032878 @default.
- W3169628166 date "2022-01-01" @default.
- W3169628166 modified "2023-09-26" @default.
- W3169628166 title "Necessary conditions for feedback stabilization and safety" @default.
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