New directions on hybrid control systems

Nonlinear control systems have undergone tremendous advances in the last two decades at the levels of theory and applications. Among those, a class of particular interest is that one resulting from the interaction of a control system with a system governed by different dynamics. This class of system lies in the hybrid and nonlinear control systems field. In the last decade, the study of such hybrid systems, whose behavior can be mathematically described using a mixture of logicbased switching and difference/differential linear or nonlinear equations, has attracted important research efforts. It is motivated by the fact that many physical systems are controlled or supervised by controllers with such mixed dynamics. In many applications (such as Automotive, Networked control systems, Energy management, Biology, etc.), analysis and design methods for systems evolving both continuously and discontinuously components are then needed. Furthermore, among many important problems formulated in the context of hybrid systems, switched control systems have been attracting much attention in recent years. A switched system is a hybrid dynamical system consisting of a family of continuous time subsystems and a rule that governs the switching between them. Many important questions that relate to their behavior still remain unanswered. Some of these questions have been characterized by NP-hardness and undecidability results. Many results are relevant not only for the community working on hybrid systems but have also many consequences in linear and nonlinear control theory. This special issue takes place in the context of hybrid systems and concerns all the aspects of analysis properties or control design problems. In accordance with the context above mentioned, the objective of this special issue aims at identifying the recent advances and the associate challenging mathematical problems regarding all the aspects of analysis properties or control design issues. Hence, the special issue covers some aspects regarding: • analysis of stability of hybrid systems; • reset control systems; • systems subject to switching operators; • design of hybrid controllers for linear or nonlinear control systems; • overcoming the limitations of classical feedbacks using nonlinear or hybrid laws; • practical and implementation aspects in nonlinear and hybrid contexts; • numerical simulations of hybrid systems; • analytical tools for hybrid optimal control.