  In many applications, the integrals and derivatives of signals carry valuable
information (e.g., cumulative success over a time window, the rate of change)
regarding the behavior of the underlying system. In this paper, we extend the
expressiveness of Signal Temporal Logic (STL) by introducing predicates that
can define rich properties related to the integral and derivative of a signal.
For control synthesis, the new predicates are encoded into mixed-integer linear
inequalities and are used in the formulation of a mixed-integer linear program
to find a trajectory that satisfies an STL specification. We discuss the
benefits of using the new predicates and illustrate them in a case study
showing the influence of the new predicates on the trajectories of an
autonomous robot.
