Modeling and analysis of hybrid systems

Project members: B. De Schutter, W.M.P.H. Heemels (Eindhoven University of Technology), A. Bemporad (ETH Zürich)

Sponsored by: SICONOS (EU project)

Hybrid systems arise from the interaction between continuous-variable systems (i.e., systems that can be described by a system of difference or differential equations) and discrete-event systems (i.e., asynchronous systems where the state transitions are initiated by events; in general the time instants at which these events occur are not equidistant). In general we could say that a hybrid system can be in one of several modes whereby in each mode the behavior of the system can be described by a system of difference or differential equations, and that the system switches from one mode to another due to the occurrence of an event (see Figure 1).

We have shown that several classes of hybrid systems: piecewise-affine systems, mixed logical dynamical systems, complementarity systems and max-min-plus-scaling systems are equivalent [3,4,22,23]. Some of the equivalences are established under (rather mild) additional assumptions. These results are of paramount importance for transferring theoretical properties and tools from one class to another, with the consequence that for the study of a particular hybrid system that belongs to any of these classes, one can choose the most convenient hybrid modeling framework. Related research is described under Project 4.9.

In addition, we have also shown an equivalence between two type of mathematical programming problems: the linear complementarity problem (LCP) and the extended linear complementarity problem (ELCP) [14]. More specifically, we have shown that an ELCP with a bounded feasible set can be recast as an LCP. This result allows us to apply existing LCP algorithms to solve ELCPs [13].