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

Control Synthesis using Signal Temporal Logic Specifications with Integral and Derivative Predicates