Study and comparison of membership-set outer bounding

When model output-error is unknown but bounded, the set of parameter called the membership-set and consistent with the measurement, the model and the error bounds is a polytope, the complexity of which is increasing with the model order and the measurement number. Such complexity bereaves the algorithm updating the polytope to be used in real time control. To overcome this complexity, the exact polytope is approximated by an outer bounding region with a simpler shape and which approximate it as most as possible. In this paper we present first algorithms which update the exact polytope and its outer bounding approximations such as ellipsoid, parallelotope or orthotope. A comparative study of these algorithms is carried out. The comparison is based on the volume of the final region, the computing and the convergence times, the numerical complexity and the updating rate