Safety critical control design for nonlinear system with tracking and safety objectives

Abstract

This paper proposes a safety critical control law for the tracking with safety of an affine nonlinear control system, which demonstrates how to sacrifice the tracking performance to keep the system trajectory in the safe zone and how to design a performance indicator function for the tradeoff between decreasing the tracking error and satisfying the safety requirement. Our design is essentially a nonlinear multi-objective control to achieve both safety and asymptotic tracking if there is no conflict between the tracking and safety, or to decrease the tracking error under the safety constraints otherwise. Different from existing methods for safety critical control problems, the design idea is to find a tracking controller without safety consideration, and then design a safety controller based on a control barrier function, which is capable of dealing with both tracking and safety issues. The efficiency of our design is illustrated by a mechanical system in both non-conflicted and conflicted cases.