REACHABILITY UNDER STATE CONSTRAINTS - THE ELLIPSOIDAL TECHNIQUE

Abstract

This report describes the calculation of the reach sets and tubes with hard bounds on the controls and state space variables, with an emphasis on linear nonautonomous systems. The topic is important in the verification of hybrid systems and navigation problems, in set-membership estimation, robust control synthesis and related fields. The suggested scheme for linear systems relies on external approximations by ellipsoidal-valued tubes and induces a smaller computational burden compared with other methods of reach set calculation. In particular such approximations may be expressed through ordinary differential equations with coefficients given in explicit analytical form. This results in exact parametric representation of reach tubes through families of external ellipsoidal tubes. A tight approximation partly requires an online solution of a recurrent optimization problem. Applications to target problems relevant for verification of complex systems are finally indicated.