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Pure Mathematics 2025
饱和控制输入下的有限时间稳定问题
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Abstract:
本文针对饱和输入约束下的一类非线性动力系统的有限时间稳定问题进行研究。基于李雅普诺夫函数理论，给出了实现有限时间稳定的充分条件，得到了有限时间稳定平衡点，估计了系统状态在饱和约束下的收敛速率以及稳定时间边界。其次，结合线性矩阵不等式理论，通过假设李雅普诺夫函数，设计了满足饱和约束的控制增益矩阵与反馈增益矩阵。
This article focuses on the finite-time stability problem of a class of nonlinear systems under actuator saturation constraints. Based on the theory of Lyapunov function, sufficient conditions for achieving finite time stability are given, and the finite time stable equilibrium point is obtained. The convergence rate and stable time boundary of the system state under saturation constraints are estimated. Secondly, based on the theory of linear matrix inequality, a control gain matrix and feedback gain matrix satisfying saturation constraints were designed by assuming a Lyapunov function.
| [1] | Dorato, P. (1961) Short Time Stability in Linear Time-Varying Systems. Polytechnic Institute of Brooklyn. |
| [2] | Yang, X., Lam, J., Ho, D.W.C. and Feng, Z. (2017) Fixed-Time Synchronization of Complex Networks with Impulsive Effects via Nonchattering Control. IEEE Transactions on Automatic Control, 62, 5511-5521. https://doi.org/10.1109/tac.2017.2691303 |
| [3] | He, X., Li, X. and Song, S. (2022) Finite-Time Input-to-State Stability of Nonlinear Impulsive Systems. Automatica, 135, Article 109994. https://doi.org/10.1016/j.automatica.2021.109994 |
| [4] | Li, X., Yang, X. and Song, S. (2019) Lyapunov Conditions for Finite-Time Stability of Time-Varying Time-Delay Systems. Automatica, 103, 135-140. https://doi.org/10.1016/j.automatica.2019.01.031 |
| [5] | Amato, F., De Tommasi, G. and Pironti, A. (2013) Necessary and Sufficient Conditions for Finite-Time Stability of Impulsive Dynamical Linear Systems. Automatica, 49, 2546-2550. https://doi.org/10.1016/j.automatica.2013.04.004 |
| [6] | Hu, T. and Lin, Z. (2001) Control Systems with Actuator Saturation: Analysis and Design. Springer Science and Business Media |
| [7] | Li, H., Jiang, Q. and Deng, H. (2023) Saturation-Degree-Dependent Event-Triggered Control for Saturated Systems. 2023 China Automation Congress (CAC), Chongqing, 17-19 November 2023, 3291-3296. https://doi.org/10.1109/cac59555.2023.10450541 |
| [8] | Li, X. and Zhu, C. (2022) Saturated Impulsive Control of Nonlinear Systems with Applications. Automatica, 142, Article 110375. https://doi.org/10.1016/j.automatica.2022.110375 |
| [9] | Saqib, N.U., Rehan, M., Hussain, M. and Zheng, Z. (2019) Observer-Based Anti-Windup Compensator Design for Nonlinear Systems. Journal of the Franklin Institute, 356, 11364-11384. https://doi.org/10.1016/j.jfranklin.2019.01.056 |
| [10] | Yan, L., Liu, Z., Chen, C.L.P., Zhang, Y. and Wu, Z. (2023) Reinforcement Learning Based Adaptive Optimal Control for Constrained Nonlinear System via a Novel State-Dependent Transformation. ISA Transactions, 133, 29-41. https://doi.org/10.1016/j.isatra.2022.07.006 |
