Hybrid Systems Described by the Complementary Formalism

In recognition of the fact that many systems contain both continuous and discrete aspects, considerable study has been devoted recently to "hybrid systems." The formulation of equations of motion for hybrid systems in explicit form, including the condition/event rules and the description of the continuous dynamics for every possible mode, is in many cases a formidable task, and there is a clear need for devices that enable the modeler to work in what might be called a "high-level language." A formalism that can be used for this purpose is the so-called complementarity formalism [5, 8, 9]. The formalism is applicable to a broad class of physical hybrid systems, as well as to hybrid systems described by an underlying dynamics subject to piecewise-linear constraints. This paper surveys some of the key issues treated in [8, 9], and discusses some possible extensions.