Complementarity modeling of hybrid systems

Complementarity modeling of hybrid systemsA

A complementarity framework is described for the modeling of certain classes of mixed continuous/discrete dynamical systems. The use of such a framework is well-known for mechanical systems with inequality constraints, but we give a more general formulation which applies for instance also to switching control systems. The main theoretical results in the paper are concerned with uniqueness of sm...

The Complementarity Class of Hybrid Dynamical Systems

This paper gives an introduction to the field of dynamical complementarity systems. A summary of their main applications and properties together with connections to other hybrid model classes is provided. Moreover, the main mathematical tools which allow one to lead studies on complementar-ity systems are presented briefly. Many examples illustrate the developments. The available results on mod...

The extended linear complementarity problem and the modeling and analysis of hybrid systems

First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We briefly discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More specifically, we consider a traffic-light-controlle...

Modeling of Hybrid Systems

Well-posedness of the Complementarity Class of Hybrid Systems

One of the most fundamental properties of any class of dynamical systems is the study of well-posedness, i.e. the existence and uniqueness of a particular type of solution trajectories given an initial state. In case of interaction between continuous dynamics and discrete transitions this issue becomes highly non-trivial. In this survey an overview is given of the well-posedness results for com...