This paper presents a systematic method for synthesizing a Control Barrier
Function (CBF) that encodes predictive information into a CBF. Unlike other
methods, the synthesized CBF can account for changes and time-variations in the
constraints even when constructed for time-invariant constraints. This avoids
recomputing the CBF when the constraint specifications change. The method
provides an explicit characterization of the extended class K function {\alpha}
that determines the dynamic properties of the CBF, and {\alpha} can even be
explicitly chosen as a design parameter in the controller synthesis. The
resulting CBF further accounts for input constraints, and its values can be
determined at any point without having to compute the CBF over the entire
domain. The synthesis method is based on a finite horizon optimal control
problem inspired by Hamilton-Jacobi reachability analysis and does not rely on
a nominal control law. The synthesized CBF is time-invariant if the constraints
are. The method poses mild assumptions on the controllability of the dynamic
system and assumes the knowledge of at least a subset of some control invariant
set. The paper provides a detailed analysis of the properties of the
synthesized CBF, including its application to time-varying constraints. A
simulation study applies the proposed approach to various dynamic systems in
the presence of time-varying constraints. The paper is accompanied by an online
available parallelized implementation of the proposed synthesis method.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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