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.

In this paper, we present a twisting control scheme with Proportional-Integral-Derivative (PID) sliding surface for a two-axis electrostatic torsional micromirror, and the utilization of the proposed scheme in a laser scanning system. The experimental results of set-point regulation verify that the proposed scheme provides enhanced transient response and positioning performance as compared to traditional sliding mode control. To evaluate the tracking performance of the closed-loop system, triangular waves with different frequencies are used as desired traces. With the proposed scheme the experimental results verified that the closed-loop controlled micromirror follows the given triangular trajectories precisely. A micromirror-based laser scanning system is developed to obtain images. When compared with open-loop control, the experimental results demonstrated that the proposed scheme is able to reduce the distortion of the raster scan, and improve the imaging performance in the presence of cross-coupling effect.