arXiv:2611.13286v1 Announce Type: new Abstract: We formulate geometric hybrid dynamical systems with states on intrinsic manifolds and inputs in topological spaces using relaxed C1-control bundles. Within this framework, we establish a barrier certificate that guarantees forward invariance of a closed set for closed-loop systems. We introduce multiple control barrier functions and derive conditions that render their sublevel sets forward invariant. We then construct pointwise optimal safe control laws, establish regularity conditions for measurable selections, and use these laws to design safety filters for geometric hybrid systems on manifolds. A second-order bouncing-pendulum example illustrates the framework and results.
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