Hybrid Systems: Theory, Computation and Applications

Theory, computation and applications define the evolution of the field of control. This premise is first illustrated with some historical examples and then with the emerging area of hybrid systems, which can be viewed, loosely speaking, as dynamical systems with switches. Many practical problems can be formulated in the hybrid system framework. Power electronics are hybrid systems by their very nature, systems with hard bounds and/or friction can be described in this manner and problems from other domains, as diverse as driver assistance systems, anesthesia and active vibration control can be put in this form. We will highlight the theoretical developments and mention the extensive software that helps to bring the theory to bear on the practical examples. We will close with an outlook for hybrid systems and control more generally.