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Volume 10 Issue 3
Mar.  2023

IEEE/CAA Journal of Automatica Sinica

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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.

# 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
• 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.

• 1 The system model comes from [50].
2 The system model comes from [50].
3 The pendulum system model comes from [78].
4 The system model comes from [83].
5 The system model and experimental parameters come from [35].
6 The system model and experimental parameters come from [32].
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