COMPLEMENTARITY MODELING OF HYBRID SYSTEMS

A complementarity framework is described for the modeling of certain c lasses of mixed continuous/discrete dynamical systems. The use of such a framework is well known for mechanical systems with inequality cons traints, but we give a more general formulation which also applies, fo r instance, to switching control systems, The main theoretical results in the paper are concerned with uniqueness of smooth continuations; t he solution of this problem requires the construction of a map from th e continuous state to the discrete state, A crucial technical tool is the so-called linear complementarity problem (LCP) from mathematical p rogramming; we introduce various generalizations of this problem.