分段仿射混杂系统可达性研究综述

Hybrid system is a kind of dynamical systems consisting of discrete event systems and continuous systems. Many practical systems, e.g., embedded systems, network systems, robotics, and power systems, can be formulated by such hybrid systems. The theory of hybrid systems is an interdiscipline of control theory, computer science and mathematics. Piecewise affine hybrid systems is a special kind of hybrid systems, consisting of linear affine systems and polyhedral domains. The reachability problem was oriented from safety problems, i.e., checking whether the trajectory will enter unsafe regions. Afterward, it focus on the problems: Can the trajectories enter final set in finite time within specific path region, or what is the largest set such that a temporal logic specification can be satisfied. The paper surveys the recent results on reachability of piecewise affine hybrid systems, and gives a perspective for the future research.