A New Safety Criterion for Dynamics Systems by Barrier Function based on Forward Invariant Set

Abstract

This paper has put a lot of effort into the enhancement the observability of the reciprocal barrier function at the boundary of forward invariant set. A exponential barrier function, which is essentially different from zeroing barrier function and can simplify the construction of barrier function without sum-of squares (SOS) programming of positive semi-definite polynomials, is designed to create a new safety criterion for a class of dynamic system. And it verifies that an exponential barrier function for its forward invariant and pre-compact set can make the system safe and uniformly asymptotically stable, even exponentially stable. Moreover, The exponential barrier function is applied to the establishment of corresponding control barrier function and control laws for a class of nonlinear dynamic control systems. Then, through simulation examples, the correctness of the theory has been visually verified.