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Controlled invariant set and viability regulation of dynamical controlsystems have played important roles in many control and coordinationapplications. In this paper we develop a temporal viability regulation theoryfor general dynamical control systems, and in particular for control affinesystems. The time-varying viable set is parameterized by time-varyingconstraint functions, with the aim to regulate a dynamical control system to beinvariant in the time-varying viable set so that temporal state-dependentconstraints are enforced. We consider both time-varying equality and inequalityconstraints in defining a temporal viable set. We also present sufficientconditions for the existence of feasible control input for the control affinesystems. The developed temporal viability regulation theory is applied tomobile vehicle coordination.

Temporal viability regulation for control affine systems with applications to mobile vehicle coordination under time-varying motion constraints