Reach set computations are of fundamental importance in control theory. We consider the reach set problem for open-loop systems described by parametric inhomogeneous linear differential systems and use real quanitfier elimination methods to get exact and approximate solutions. For simple elementary functions we give an exact calculation of the cases where exact semialgebraic transcendental implicitization is possible. For the negative cases we provide approximate alternating using discrete point checking or safe estimations of reach sets and control parameter sets. The method employs a reduction of forward and backward reach set and control parameter set problem to the transcendental implicitization problem for the components of special solutions of simpler non-parametric systems. Numerous examples are computed using the REDLOG and QEPCAD packages.
Erika Cetindag