Explicit Solution of Tunable Input-to-State Safe-Based Controller Under High-Relative-Degree Constraints

2025/03/10 by Wei, Yan, Feng, Yu, Ou, Linlin +2
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2503.07007

Abstract

This paper investigates the safety analysis and verification of nonlinear systems subject to high-relative-degree constraints and unknown disturbance. The closed-form solution of the high-order control barrier functions (HOCBF) optimization problem with and without a nominal controller is first provided, making it unnecessary to solve the quadratic program problem online and facilitating the analysis. Further, we introduce the concept of tunable input-to-state safety(ISSf), and a new tunable function in conjunction with HOCBF is provided. When combined with the existing ISSf theorem, produces controllers for constrained nonlinear systems with external disturbances. The theoretical results are proven and supported by numerical simulations.

Related

• Universal Barrier Functions for Safety and Stability of Constrained Nonlinear Systems
• Control Barrier Functions for Systems with Multiple Control Inputs
• Control Barrier Functions for Systems with High Relative Degree
• Safety Critical Control for Nonlinear Systems with Complex Input Constraints
• Control Barrier Functions-based Semi-Definite Programs (CBF-SDPs): Robust Safe Control For Dynamic Systems with Relative Degree Two Safety Indices