  Cyber-physical systems (CPS) are systems that interact with the physical
world via sensors and actuators. In such a system, the reading of a sensor
represents measures of a physical quantity, and sensor values are often reals
ranged over bounded intervals. The implementation of control laws is based on
nonlinear numerical computations over the received sensor values. Synthesizing
controllers fulfilling features within CPS brings a huge challenge to the
research community in formal methods, as most of the works in automatic
controller synthesis (LTL synthesis) are restricted to specifications having a
few discrete inputs within the Boolean domain.
  In this report, we present a novel approach that addresses the above
challenge to synthesize controllers for CPS. Our core methodology, called
numerical LTL synthesis, extends LTL synthesis by using inputs or outputs in
real numbers and by allowing predicates of polynomial constraints to be defined
within an LTL formula as specification. The synthesis algorithm is based on an
interplay between an LTL synthesis engine which handles the pseudo-Boolean
structure, together with a nonlinear constraint validity checker which tests
the (in)feasibility of a (counter-)strategy. The methodology is integrated
within the CPS research framework Ptolemy II via the development of an LTL
synthesis module G4LTL and a validity checker JBernstein. Although we only
target the theory of nonlinear real arithmetic, the use of pseudo-Boolean
synthesis framework also allows an easy extension to embed a richer set of
theories, making the technique applicable to a much broader audience.
