Safety Control of Switched Systems via Multiple Barrier Functions

This article is concerned with the problem of safety control for switched systems, where different safe sets are allowed for different subsystems and safety is not necessarily possessed for subsystems. A necessary and sufficient condition is presented for safety of switched systems by exploiting a multiple barrier functions (MBFs) method. To reveal the relationship about safety between subsystems and switched systems, an extended Nagumo's Theorem in the switched systems framework is derived. Also, several switched control design conditions are respectively provided to ensure safety of switched systems. Based on the union of MBFs and multiple Lyapunov functions, a novel safety-critical control framework is established to simultaneously ensure safety and stability of switched systems. Also, an auxiliary cost function is introduced to transform the safety-critical optimal control problem of switched systems into the one of non-switched systems. Finally, two examples are illustrated to demonstrate the effectiveness of the proposed methods.