  In this paper, a method to synthesize controllers using finite time
convergence control barrier functions guided by linear temporal logic
specifications for continuous time multi-agent dynamical systems is proposed.
Finite time convergence to a desired set in the state space is guaranteed under
the existence of a suitable finite time convergence control barrier function.
In addition, these barrier functions also guarantee forward invariance once the
system converges to the desired set. This allows us to formulate a theoretical
framework which synthesizes controllers for the multi-agent system. These
properties also enable us to solve the reachability problem in continuous time
by formulating a theorem on the composition of multiple finite time convergence
control barrier functions. This approach is more flexible than existing methods
and also allows for a greater set of feasible control laws. Linear temporal
logic is used to specify complex task specifications that need to be satisfied
by the multi-agent system. With this solution methodology, a control law is
synthesized that satisfies the given temporal logic task specification. Robotic
experiments are provided which were performed on the Robotarium multi-robot
testbed at Georgia Tech.
