High‐order control barrier functions‐based optimization control for time‐varying nonlinear systems with full‐state constraints: A dynamic sub‐safe set approach

Author:

Wang Haijing1ORCID,Peng Jinzhu1ORCID,Xu Juanjuan2ORCID,Zhang Fangfang1ORCID,Wang Yaonan13

Affiliation:

1. School of Electrical and Information Engineering Zhengzhou University Zhengzhou China

2. School of Control Science and Engineering Shandong University Jinan China

3. College of Electrical and Information Engineering Hunan University Changsha China

Abstract

SummaryThis study focuses on the problems of safety control and stabilization for time‐varying nonlinear systems in the presence of time‐varying full‐state constraints. High‐order control barrier functions (HoCBFs) without the assumption of forward completeness are introduced to prevent high‐relative degree constraint violations. The activated HoCBFs, which determine the dynamic sub‐safe sets, are proposed to indicate that the state constraints are already or about to be violated. Subsequently, the HoCBFs‐based controller is designed to obtain the admissible control set by utilizing the quadratic programming (QP) with activated HoCBFs conditions to synthesize the nominal controller. An explicit analytical expression is provided for the HoCBFs‐based controller. The input‐to‐state stable (ISS) property of the closed‐loop system under the proposed controller is investigated to ensure that all closed‐loop states remain bounded and achieve asymptotic tracking without violation of the constraint. Moreover, a Lyapunov‐like constraint is added to the HoCBFs‐based QP problem such that the solvability of the QP problem is a sufficient condition for the system ISS. The effectiveness of the proposed HoCBFs‐based control method for time‐varying nonlinear systems is illustrated using a numerical example.

Funder

National Natural Science Foundation of China

Publisher

Wiley

Subject

Electrical and Electronic Engineering,Industrial and Manufacturing Engineering,Mechanical Engineering,Aerospace Engineering,Biomedical Engineering,General Chemical Engineering,Control and Systems Engineering

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1. Real-Time Safety Index Adaptation for Parameter-Varying Systems via Determinant Gradient Ascend;2024 American Control Conference (ACC);2024-07-10

2. Safety-Based Dynamic Output Feedback Tracking Control of Time-Varying Input–Output Linearizable Systems With Output Constraints;IEEE Transactions on Circuits and Systems II: Express Briefs;2024-01

3. Adaptive Safety Control of a Constrained Uncertain Robotic System;2023 8th International Conference on Automation, Control and Robotics Engineering (CACRE);2023-07

4. Robust High-Order Control Barrier Functions-Based Optimal Control for Constrained Nonlinear Systems With Safety-Stability Perspectives;IEEE Transactions on Automation Science and Engineering;2023

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