Safety-critical multi-tasks control for switched systems via several barrier functions

Abstract

This paper investigates the problem of safety-critical multi-tasks control (SCMTC) for switched systems, where the multi-tasks control is achieved by ensuring the invariance and attraction of the task set. A new definition of safety is presented under the switched systems framework, which extends the existing safety definition for non-switched systems and reveals the essence of safety for switched systems. For two different types of task sets, a single barrier function (SBF) method and a multiple barrier functions method are proposed to solve the SCMTC problem, where the former requires each task set to be defined by a continuously differentiable function, while the latter requires that to be defined by multiple continuously differentiable functions. Both the two methods allow the safety and/or the invariance and attraction of the task sets to be unnecessary for individual subsystems. Also, two novel task-based switching signals are designed to guide the switching among subsystems that do not possess the invariance and attraction of task sets. Furthermore, a common barrier function method, as a special case of the SBF method, is proposed to solve the SCMTC problem for switched systems under arbitrary switchings. Finally, an illustrate example is given to verify the effectiveness of the proposed methods.