Efficient Modeling of Hybrid Systems

This book deals with modeling of systems which combine continuous dynamics with discrete logic. Such systems are called hybrid systems. We highlight several theoretical frameworks for modeling of hybrid systems. In particular, we cover discrete hybrid automata, piecewise affine systems and mixed logical dynamical systems. Aim of this book is to investigate and propose an efficient mathematical framework for modeling of hybrid systems represented either as discrete hybrid automata or piecewise affine systems. It is known that models involving integer or logical variables can be transformed into a mixed integer programming (MIP) problem. As a main tool for translating these logical statements into the equivalent MIP form we investigate the so-called big-M modeling technique. Traditionally, integer variables are encoded in the MIP problem by assigning one binary variable to each possible value of the integer. Contribution of this book lies in an alternative approach, where integer variables can be modeled by fewer binary variables, which only requires logarithmical number of original binary variables.