  The use of spatio-temporal logics in control is motivated by the need to
impose complex spatial and temporal behavior on dynamical systems, and to
control these systems accordingly. Synthesizing correct-by-design control laws
is a challenging task resulting in computationally demanding methods. We
consider efficient automata-based planning for continuous-time systems under
signal interval temporal logic specifications, an expressive fragment of signal
temporal logic. The planning is based on recent results for automata-based
verification of metric interval temporal logic. A timed signal transducer is
obtained accepting all Boolean signals that satisfy a metric interval temporal
logic specification, which is abstracted from the signal interval temporal
logic specification at hand. This transducer is modified to account for the
spatial properties of the signal interval temporal logic specification,
characterizing all real-valued signals that satisfy this specification. Using
logic-based feedback control laws, such as the ones we have presented in
earlier works, we then provide an abstraction of the system that, in a suitable
way, aligns with the modified timed signal transducer. This allows to avoid the
state space explosion that is typically induced by forming a product automaton
between an abstraction of the system and the specification.
