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Volume 10 Issue 3
Mar.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Contents
B. Q. Li, S. P. Wen, Z. Yan, G. H. Wen, and T. W. Huang, “A survey on the control Lyapunov function and control barrier function for nonlinear-affine control systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 584–602, Mar. 2023. doi: 10.1109/JAS.2023.123075
Citation: B. Q. Li, S. P. Wen, Z. Yan, G. H. Wen, and T. W. Huang, “A survey on the control Lyapunov function and control barrier function for nonlinear-affine control systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 584–602, Mar. 2023. doi: 10.1109/JAS.2023.123075

A Survey on the Control Lyapunov Function and Control Barrier Function for Nonlinear-Affine Control Systems

doi: 10.1109/JAS.2023.123075
Funds:  This work was supported in part by the National Natural Science Foundation of China (U22B2046, 62073079, 62088101), in part by the General Joint Fund of the Equipment Advance Research Program of Ministry of Education (8091B022114), and in part by NPRP (NPRP 9-466-1-103) from Qatar National Research Fund
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  • This survey provides a brief overview on the control Lyapunov function (CLF) and control barrier function (CBF) for general nonlinear-affine control systems. The problem of control is formulated as an optimization problem where the optimal control policy is derived by solving a constrained quadratic programming (QP) problem. The CLF and CBF respectively characterize the stability objective and the safety objective for the nonlinear control systems. These objectives imply important properties including controllability, convergence, and robustness of control problems. Under this framework, optimal control corresponds to the minimal solution to a constrained QP problem. When uncertainties are explicitly considered, the setting of the CLF and CBF is proposed to study the input-to-state stability and input-to-state safety and to analyze the effect of disturbances. The recent theoretic progress and novel applications of CLF and CBF are systematically reviewed and discussed in this paper. Finally, we provide research directions that are significant for the advance of knowledge in this area.

     

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    Highlights

    • Core findings: This survey provides a brief overview on the control problems of general nonlinear-affine control systems with the help of control Lyapunov function (CLF) and control barrier function (CBF). The control objectives are formulated as solving a constrained quadratic programming (QP) problem. Uncertainties are also considered in this paper, where the robustness of CLF-CBF-based QP is analyzed to study the effect of disturbances. The recent theoretical progress and novel applications of CLF and CBF are reviewed
    • Essence of the research: As two essential performances of control systems, stability and safety could be achieved by any controller satisfying CLF and CBF conditions, respectively. This survey combines the CLF and CBF with the QP optimization framework to obtain the optimal control protocol for general nonlinear-affine control systems, under which both stability and safety are ensured and the cost function gets its minimum value at the same time
    • Distinction of the paper: This survey reveals the contributions of CLF-CBF-based QP on the performances of nonlinear-affine control systems and reviews the recent theoretical progress and novel applications. Some interesting and challenging topics are proposed in this paper, which may be potential research directions in the future

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