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摘要: 2017年, 宋永端教授团队于Automatica发表高阶非线性系统预设时间控制的原创性工作. 不同于传统控制方法, 该策略能够人为预先设定系统收敛的时间, 同时具备出色的扰动抑制性能, 成果面世后迅速成为研究热点, 国内外学者围绕该方向已开展大量深入研究. 从系统稳定性相关的基本概念出发, 系统辨析有限时间、固定时间、预定时间与预设时间稳定性之间的联系与区别, 进而聚焦于预设时间控制的实现途径. 以经典的比例制导、终端约束最优控制、滑模控制等为基础, 梳理其理论渊源, 重点阐述状态变换、时间尺度变换、复合反馈及周期时滞反馈等核心设计框架. 通过比较不同方法的收敛性能, 进一步分析增强或削弱反馈信号对系统性能与工程可实现性的影响. 此外, 还讨论预设时间控制中存在的数值奇异和噪声敏感等挑战, 总结多种解决方案, 并对未来在理论融合、智能控制、跨领域应用验证等方面的发展方向进行展望. 预设时间控制在航空航天、机器人、多智能体等对动态性能与时间精度要求严苛的领域中展现出重要应用潜力, 其进一步发展将推动高可靠控制系统的工程实现.Abstract: In 2017, Professor Song Yong-Duan's team published an original work on predefined-time control of high-order nonlinear systems in Automatica. Unlike traditional control methods, this strategy enables the system convergence time to be artificially prespecified while exhibiting excellent disturbance rejection performance. Upon its release, it quickly became a research hotspot, prompting extensive follow-up studies worldwide. This paper begins with the fundamental concepts related to system stability, systematically analyzes the connections and distinctions among finite-time, fixed-time, predefined-time, and prescribed-time stability, and then focuses on the implementation approaches of prescribed-time control. Building on classical proportional navigation, optimal control with terminal constraint, and sliding mode control, etc., this paper traces their theoretical origins and elaborates on core design frameworks such as state transformation, time-scale transformation, composite feedback, and periodic time-delay feedback. By comparing the convergence performance of different methods, it further analyzes the impact of enhancing or weakening feedback signals on system performance and engineering feasibility. Additionally, the paper discusses the challenges in prescribed-time control, such as numerical singularities and noise sensitivity, summarizes various solutions, and prospects future development directions, including theoretical integration, intelligent control, and cross-domain application validation. Prescribed-time control demonstrates significant application potential in fields with stringent requirements for dynamic performance and temporal precision, such as aerospace, robotics, and multi-agent systems. Its further development will advance the engineering implementation of high-reliability control systems.
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Key words:
- Prescribed-time control /
- Stability /
- Control theory
1)1 1符号$ \|{\boldsymbol{d}}(\tau)\| $定义为$ \|{\boldsymbol{d}}(\tau)\|=\sup_{0 \leq \tau \leq t_f} |{\boldsymbol{d}}(\tau)| $.2)2 2在有限时间控制相关文献中, “有限时间稳定”通常默认平衡点不仅是稳定的而且是吸引的, 即会在有限时间内收敛到0. 对于平衡点非吸引但系统状态可在有限时间内进入并保持于原点某邻域内的情况, 则多被称为“实用有限时间稳定”. 如注2所述, 相较于数学描述, 纯文字表述易引发歧义, 因此在阅读文献时需结合具体语境仔细辨析.3)3 3为描述简洁, 后文中提到的“稳定”均指“全局一致渐近稳定”. -
图 3 有限时间、固定时间、预定时间、预设时间稳定的关系
Fig. 3 Relationships among finite-time, fixed-time, predefined-time, and prescribed-time stability
图 6 周期时滞反馈控制下的增益和输出信号示意图
Fig. 6 Schematic diagram of control gain and output under periodic delayed feedback control
图 7 有限时间控制下的系统状态与控制输入轨迹
Fig. 7 State and control input responses under finite-time control
图 10 预设时间控制下的系统状态与控制输入轨迹
Fig. 10 State and control input responses under prescribed-time control
图 8 固定时间控制下的系统状态与控制输入轨迹
Fig. 8 State and control input responses under fixed-time control
图 9 预定时间控制下的系统状态与控制输入轨迹
Fig. 9 State and control input responses under predefined-time control
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[1] 刘强, 张汉锋, 陈俊儒. 反弹道导弹作战研究. 北京: 国防工业出版社, 2018. [2] Liu Y. Homing and navigational courses of automatic target-seeking devices. Journal of Applied Physics, 1948, 19(12): 1122−1128 doi: 10.1063/1.1715028 [3] 谢力, 张奕群. 袁家骝在无线电定向和导航方面的早期工作. 系统与控制纵横, 2015, 2(2): 11−23 [4] Ho Y, Bryson A, Baron S. Differential games and optimal pursuit-evasion strategies. IEEE Transactions on Automatic Control, 1965, 10(4): 385−389 [5] Sidar M. On closed-loop optimal control. IEEE Transactions on Automatic Control, 1964, 9(3): 292−293 doi: 10.1109/TAC.1964.1105719 [6] Åström K. Early control development in Sweden. European Journal of Control, 2007, 13: 7−19 doi: 10.3166/ejc.13.7-19 [7] 吴加望. “爱国者”TVM制导体制分析. 现代防御技术, 1992(1): 49−59 [8] 徐文旭. “爱国者”导弹拦截战术弹道导弹的概率. 战术导弹技术, 1999(1): 33−37 [9] Zarchan P. Tactical and Strategic Missile Guidance. 6th ed. Reston, VA, USA: American Institute of Aeronautics and Astronautics, 2012. [10] Song Y, Wang Y, Holloway J, Krstic M. Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time. Automatica, 2017, 83: 243−251 doi: 10.1016/j.automatica.2017.06.008 [11] H. Ye and Y. Song. Prescribed-time tracking control of MIMO nonlinear systems with non-vanishing uncertainties. IEEE Transactions on Automatic Control, 2023, 68(6): 3664−3671 doi: 10.1109/TAC.2022.3194100 [12] Bertino A, Naseradinmousavi P, Krstic M. Design and experiment of a prescribed-time trajectory tracking controller for a 7-dof robot manipulator. Journal of Dynamic Systems, Measurement, and Control, 2022, 144(10): 101005 doi: 10.1115/1.4055023 [13] Ye H, Wen C, Lam J, Ioannou P. Decentralized prescribed-time input-to-state stabilization for interconnected normal form nonlinear systems. Automatica, 2025, 180: 112480 doi: 10.1016/j.automatica.2025.112480 [14] Wang Y, Song Y, Hill D, Krstic M. Prescribed-time consensus and containment control of networked multiagent systems. IEEE Transactions on Cybernetics, 2019, 49(4): 1138−1147 doi: 10.1109/TCYB.2017.2788874 [15] Shakouri A, Assadian N. Prescribed-time control with linear decay for nonlinear systems. IEEE Control Systems Letters, 2022, 6: 313−318 doi: 10.1109/LCSYS.2021.3073346 [16] Zhou B. Finite-time stability analysis and stabilization by bounded linear time-varying feedback. Automatica, 2020, 121(3): 109191 doi: 10.1016/j.automatica.2020.109191 [17] Orlov Y, Kairuz R, Aguilar L. Scaling technique for prescribed-time output feedback stabilization: Autonomous and non-autonomous paradigms and their comparative study. Journal of the Franklin Institute, 2024, 361(5): 106642 doi: 10.1016/j.jfranklin.2024.01.043 [18] Kan Z, Yucelen T, Doucette E, Pasiliao E. A finite-time consensus framework over time-varying graph topologies with temporal constraints. Journal of Dynamic Systems Measurement and Control, 2017, 139(7): 071012 doi: 10.1115/1.4035612 [19] Krishnamurthy P, Khorrami F, Krstic M. A dynamic high-gain design for prescribed-time regulation of nonlinear systems. Automatica, 2020, 115(12): 108860 doi: 10.1016/j.automatica.2020.108860 [20] Krishnamurthy P, Khorrami F, Krstic M. Robust adaptive prescribed-time stabilization via output feedback for uncertain nonlinear strict-feedback-like systems. European Journal of Control, 2020, 55: 14−23 doi: 10.1016/j.ejcon.2019.09.005 [21] Krishnamurthy P, Khorrami F, Krstic M. Adaptive output-feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states. International Journal of Adaptive Control and Signal Processing, 2021, 35(2): 184−202 doi: 10.1002/acs.3193 [22] Ye H, Song Y. Prescribed-time control for time-varying nonlinear systems: A temporal scaling based robust adaptive approach. Systems and Control Letters, 2023, 181(5): 105602 doi: 10.2139/ssrn.4300025 [23] Yu J, Zhao Y, Wen C, Wu Y. A prescribed-time convergence criterion with application to adaptive control for parametric strict-feedback systems. Journal of Control and Decision, 2026, doi: 10.1080/23307706.2026.2674066. [24] Tran D, Yucelen T. Finite-time control of perturbed dynamical systems based on a generalized time transformation approach. IEEE Control Systems Letters, 2020, 136(5): 104605 doi: 10.1016/j.sysconle.2019.104605 [25] Liu C, Liu Y. Conditions and synthesis of adaptive prescribed-time controllers. IEEE Transactions on Automatic Control, 2023, 68(12): 8005−8012 doi: 10.1109/TAC.2023.3254371 [26] Wang Y, Liu Y. Adaptive prescribed-time stabilization for uncertain unmeasured-state-dependent systems. Systems & Control Letters, 2025, 204: 106228 doi: 10.1016/j.sysconle.2025.106228 [27] Wang Y, Liu Y. Prescribed-time control via dynamic-high-gain output feedback. International Journal of Robust and Nonlinear Control, 2025, 35(2): 591−603 doi: 10.1002/rnc.7665 [28] Yilmaz C. Krstic M. Prescribed-time extremum seeking for delays and PDEs using chirpy probing. IEEE Transactions on Automatic Control, 2024, 69(11): 7710−7725 doi: 10.1109/TAC.2024.3397162 [29] Kairuz R, Orlov Y, Aguilar L. Prescribed-time stabilization of controllable planar systems using switched state feedback. IEEE Control Systems Letters, 2021, 5(6): 2048−2053 doi: 10.1109/LCSYS.2020.3046682 [30] Orlov Y. Time space deformation approach to prescribed-time stabilization: Synergy of time-varying and non-Lipschitz feedback designs. Automatica, 2022, 144(4): 110485 doi: 10.1016/j.automatica.2022.110485 [31] Su J, Song Y. Prescribed-time control with bounded feedback gain: A nonscaling and structural adaptation-based approach. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2025, 55(4): 2580−2589 doi: 10.1109/TSMC.2024.3525296 [32] Yang H, Wang Y. Finite-gain based prescribed-time consensus control for multi-agent systems under switching topology. Automatica, 2026, 183: 112686 doi: 10.1016/j.automatica.2025.112686 [33] Yang H, Wang Y, Shao Z. Event-triggered prescribed-time control for a class of uncertain nonlinear systems using finite time-varying gain. ISA Transactions, 2024, 152: 167−176 doi: 10.1016/j.isatra.2024.06.012 [34] Xiao Y, Yang Y, Ye D, Zhao Y. Scaling-transformation-based attitude tracking control for rigid spacecraft with prescribed time and prescribed bound. IEEE Transactions on Aerospace and Electronic Systems, 2025, 61(1): 433−442 doi: 10.1109/TAES.2024.3451454 [35] Hu Y, Cai X, Cheng C, Shi S, Du H, Zhou H. Prescribed-time state and extended disturbance observer with application to active vibration isolation systems. IEEE/ASME Transactions on Mechatronics, 2025, 30(5): 3374−3383 doi: 10.1109/TMECH.2024.3466861 [36] Li J, Sun Z, Wang Z, Chen C. A framework of event-triggered prescribed-time stabilization of time-varying nonlinear systems and its application in tunnel diode circuit. IEEE Transactions on Circuits and Systems I: Regular Papers, 2025, 72(7): 3595−3605 doi: 10.1109/TCSI.2024.3517638 [37] Zhou B, Michiels W, Chen J. Fixed-time stabilization of linear delay systems by smooth periodic delayed feedback. IEEE Transactions on Automatic Control, 2022, 67(2): 557−573 doi: 10.1109/TAC.2021.3051262 [38] Ding Y, Zhou B, Shi Y. Prescribed-time control via periodic delayed feedback based super-twisting sliding mode algorithm. IEEE Transactions on Automatic Control, 2026, 71(3): 1813−1828 doi: 10.1109/TAC.2025.3618707 [39] Ding Y, Zhou B, Zhang K K, Michiels W. Strong prescribed-time stabilization of uncertain nonlinear systems by periodic delayed feedback. IEEE Transactions on Automatic Control, 2023, 69(6): 4072−4079 [40] Li H, Zhou B, Michiels W, Duan G R. Prescribed-time unknown input observers design by using periodic delayed output with application to fault estimation. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(2): 664−674 doi: 10.1109/TSMC.2022.3187018 [41] Espitia N, Perruquetti W. Predictor-feedback prescribed-time stabilization of LTI systems with input delay. IEEE Transactions on Automatic Control, 2021, 67(6): 2784−2799 [42] Li W, Krstic M. Prescribed-time output-feedback control of stochastic nonlinear systems. IEEE Transactions on Automatic Control, 2022, 68(3): 1431−1446 [43] Li W, Krstic M. Stochastic nonlinear prescribed-time stabilization and inverse optimality. IEEE Transactions on Automatic Control, 2022, 67(3): 1179−1193 doi: 10.1109/TAC.2021.3061646 [44] Li W, Krstic M. Prescribed-time practical inverse optimal output tracking control of stochastic nonlinear systems. SIAM Journal on Control and Optimization, 2025, 63(3): 1929−1949 doi: 10.1137/24M1671839 [45] Hua C, Ning P, Li K. Adaptive prescribed-time control for a class of uncertain nonlinear systems. IEEE Transactions on Automatic Control, 2021, 67(11): 6159−6166 doi: 10.22541/au.168655375.54524632/v1 [46] Ning P, Hua C, Li K, Meng R. A novel theorem for prescribed-time control of nonlinear uncertain time-delay systems. Automatica, 2023, 152: 111009 doi: 10.1016/j.automatica.2023.111009 [47] Abel I, Steeves D, Krstic M, Jankovic M. Prescribed-time safety design for strict-feedback nonlinear systems. IEEE Transactions on Automatic Control, 2023, 69(3): 1464−1479 [48] Chen H, Wang P, Tang G. Prescribed-time control for hypersonic morphing vehicles with state error constraints and uncertainties. Aerospace Science and Technology, 2023, 142(9): 108671 doi: 10.1016/j.ast.2023.108671 [49] 张康康, 周彬, 蔡光斌, 侯明哲. 高超声速飞行器指定时间时变高增益反馈跟踪控制. 自动化学报, 2024, 50(6): 1151−1159 [50] Pal A, Kamal S, Nagar S, Bandyopadhyay B, Fridman L. Design of controllers with arbitrary convergence time. Automatica, 2020, 112: 108710 doi: 10.1016/j.automatica.2019.108710 [51] Ye H, Song Y, Lam J, Ioannou P A. Decentralized prescribed-time control of robotic arm-finger systems for grasping and moving tasks. IEEE Transactions on Cybernetics, 2025, 55(9): 4386−4399 doi: 10.1109/TCYB.2025.3586153 [52] Zhao X, Song Y, Ye H. Adaptive distributed event-triggered cooperative manipulation of multiple manipulators under partial time-interval error constraints. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2025, 55(12): 9309−9323 doi: 10.1109/TSMC.2025.3616150 [53] Singh V, Kamal S, Ghosh S. Prescribed-time constrained feedback control for an uncertain twin rotor helicopter. Aerospace Science and Technology, 2023, 140: 108483 doi: 10.1016/j.ast.2023.108483 [54] Li S, Zhang Y, Wang X, Wang S, Duan H. Prescribed-time bearing-based formation control of underactuated asvs under external disturbance. IEEE Transactions on Circuits and Systems II: Express Briefs, 2023, 71(3): 1196−1200 doi: 10.1109/tcsii.2023.3325435 [55] Ge M, Xu H, Song Q. Prescribed-time control of four-wheel independently driven skid-steering mobile robots with prescribed performance. Nonlinear Dynamics, 2023, 111(22): 20991−21005 doi: 10.1007/s11071-023-08926-5 [56] Zhang T, Zhang S, Guo F, Zhao X, Zhang F. Prescribed time attitude containment control for satellite cluster with bounded disturbances. ISA transactions, 2022, 137(5): 160−174 doi: 10.1016/j.isatra.2022.12.018 [57] Zhou B, Zhang K K. A linear time-varying inequality approach for prescribed time stability and stabilization. IEEE Transactions on Cybernetics, 2022, 53(3): 1880−1889 [58] Dong J, Zhou B. Prescribed-time fault-tolerant control of linear time-varying systems by linear time-varying feedback. International Journal of Robust and Nonlinear Control, 2025, 35(9): 3509−3522 doi: 10.1002/rnc.7861 [59] Obuz S, Selim E, Tatlicioglu E, Zergeroglu E. Robust prescribed time control of Euler–Lagrange systems. IEEE Transactions on Industrial Electronics, 2025, 72(2): 1694−1701 doi: 10.1109/TIE.2024.3417995 [60] Ye H, Liu C, Lam J, Song Y, Kwok K, Zhou Y. A non-conservative prescribed-time control approach for robotic manipulation: Design and experiment. IEEE Transactions on Industrial Electronics, 2026. (in press [61] Pan C, Peng Z, Yang S, Wen G, Huang T. Adaptive neural network-based prescribed-time observer for battery state-of-charge estimation. IEEE Transactions on Power Electronics, 2022, 38(1): 165−176 [62] Shi Z, Feng Z, Wang Q, Dong X, Lv J, Ren Z, Wang D. Prescribed-time time-varying output formation tracking for heterogeneous multi-agent systems. IEEE Internet of Things Journal, 2024, 12(9): 11622−11632 [63] Khalil H. Nonlinear Systems. Englewood Cliffs, NJ, USA: Prentice Hall, 2002. [64] 李世华, 丁世宏, 田玉平. 一类二阶非线性系统的有限时间状态反馈镇定方法. 自动化学报, 2007, 33(070118): 101 [65] Bhat S, Bernstein D. Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Transactions on Automatic Control, 1998, 43(5): 678−682 doi: 10.1109/9.668834 [66] Polyakov A. Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control, 2012, 57(8): 2106−2110 doi: 10.1109/TAC.2011.2179869 [67] 高振宇, 郭戈. 基于扰动观测器的AUVs固定时间编队控制. 自动化学报, 2019, 45(6): 1094−1102 doi: 10.16383/j.aas.c180809 [68] Sánchez-Torres J, Gómez-Gutiérrez D, López E, Loukianov A. A class of predefined-time stable dynamical systems. IMA Journal of Mathematical Control and Information, 2018, 35(1): 1−29 doi: 10.1093/imamci/dnx004 [69] Johnson C, Gibson J. Singular solutions in problems of optimal control. IEEE Transactions on Automatic Control, 1963, 8(1): 4−15 doi: 10.1109/TAC.1963.1105505 [70] Rose N, Bronson R. On optimal terminal control. IEEE Transactions on Automatic Control, 1969, 14(5): 443−448 doi: 10.1109/TAC.1969.1099284 [71] Lewis F. Optimal Control. New York: Wiley, 1986. [72] Utkin V, Poznyak A, Orlov Y, Polyakov A. Conventional and high order sliding mode control. Journal of the Franklin Institute, 2020, 357(15): 10244−10261 doi: 10.1016/j.jfranklin.2020.06.018 [73] Lee H, Utkin V. Chattering suppression methods in sliding mode control systems. Annual Reviews in Control, 2007, 31(2): 179−188 doi: 10.1016/j.arcontrol.2007.08.001 [74] Pontryagin L. The Mathematical Theory Of Optimal Processes. John Wiley & Sons, Inc, 1962. [75] Wang L. Model Predictive Control System Design and Implementation Using MATLAB. New York, NY, USA: Springer-Verlag, 2009. [76] Song Y, Ye H, Lewis F. Prescribed-time control and its latest developments. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(7): 4102−4116 doi: 10.1109/TSMC.2023.3240751 [77] Espitia N, Poveda J, Krstic M. Prescribed-time Newton extremum seeking using delays and time-periodic gains. IEEE Transactions on Automatic Control, 2026. (in press [78] Chen Z, Ju X, Wang Z, Li Q. The prescribed time sliding mode control for attitude tracking of spacecraft. Asian Journal of Control, 2022, 24(4): 1650−1662 doi: 10.1002/asjc.2569 [79] Ye H, Song Y. Prescribed-time control for linear systems in canonical form via nonlinear feedback. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(2): 1126−1135 doi: 10.1109/TSMC.2022.3194908 [80] Ning P, Dashkovskiy S, Hua C, Li K. Dual-gain function based prescribed-time output feedback control for nonlinear time-delay systems. SIAM Journal on Control and Optimization, 2024, 62(4): 2254−2272 doi: 10.1137/23M1556496 [81] Ye H, Wen C, Song Y. Decentralized prescribed-time control for interconnected nonlinear systems via output-feedback. Automatica, 2024, 163: 111571 doi: 10.1016/j.automatica.2024.111571 [82] Song Y, Su J. A unified Lyapunov characterization for finite time control and prescribed time control. International Journal of Robust and Nonlinear Control, 2022, 33(4): 2930−2949 [83] Li J, Sun Z, Wen C, Chen C. Prescribed-time stabilization of high-order polynomial time-varying nonlinear systems. IEEE Transactions on Cybernetics, 2025, 55(3): 1301−1309 doi: 10.1109/TCYB.2024.3524366 [84] Zhou B, Shi Y. Prescribed-time stabilization of a class of nonlinear systems by linear time-varying feedback. IEEE Transactions on Automatic Control, 2021, 66(12): 6123−6130 doi: 10.1109/TAC.2021.3061645 [85] Zhang K-K, Zhou B, Duan G. Global prescribed-time output feedback control of a class of uncertain nonlinear systems by linear time-varying feedback. Automatica, 2024, 165: 111680 doi: 10.1016/j.automatica.2024.111680 [86] Zhang K-K, Zhou B, Duan G. Prescribed-time input-to-state stabilization of normal nonlinear systems by bounded time-varying feedback. IEEE Transactions on Circuits and Systems I: Regular Papers, 2022, 69(9): 3715−3725 doi: 10.1109/TCSI.2022.3182884 [87] Zhang K-K, Zhou B, Hou M, Duan G. Prescribed-time control of high-order nonholonomic systems in chained form by time-varying feedback. Systems & Control Letters, 2022, 166: 105307 doi: 10.1016/j.sysconle.2022.105307 [88] Ye H, Wen C, Song Y. Decentralized and distributed control of large-scale interconnected multi-agent systems in prescribed time. IEEE Transactions on Automatic Control, 2025, 70(2): 1115−1130 doi: 10.1109/TAC.2024.3451213 [89] Ye H, Wen C, Song Y. Distributed matrix pencil formulations for prescribed-time leader-following consensus of MASs with unknown sensor sensitivity. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2026, 56(1): 629−641 doi: 10.1109/TSMC.2025.3627671 [90] Tan Y, Ye H, Wen C, Song Y. Decentralized prescribed-time output-feedback control for interconnected systems with coupled nonidentical subsystems of different order. IEEE/CAA Journal of Automatica Sinica, 2026, 13(5): 1−11 doi: 10.1109/jas.2025.125918 [91] Ye H, Song Y. A separation principle for the prescribed-time stabilization of a class of nonlinear systems. Automatica, 2025, 171: 111983 doi: 10.1016/j.automatica.2024.111983 [92] Zuo G, Wang Y. Adaptive prescribed finite time control for strict-feedback systems. IEEE Transactions on Automatic Control, 2022, 68(9): 5729−5736 [93] Ye H, Song Y. Backstepping design embedded with time-varying command filters. IEEE Transactions on Circuits and Systems II: Express Briefs, 2022, 69(6): 2832−2836 doi: 10.1109/tcsii.2022.3144593 [94] Zuo G, Li M, Wang Y, Zhu L, Song Y. Achieving convex optimization within prescribed time for networked Euler-Lagrange systems: A novel adaptive distributed approach with small-gain conditions. IEEE Transactions on Cybernetics, 2026, 56(1): 509−522 doi: 10.1109/TCYB.2025.3611131 [95] Yu J, Li C, Ding Z, Wu Y. Adaptive prescribed-time control for nonlinear cascade systems with FXT-ISS inverse dynamics. Automatica, 2025, 182: 112527 doi: 10.1016/j.automatica.2025.112527 [96] Wang J, Liu J, Li Y, Chen C P L, Liu Z, Li F. Prescribed time fuzzy adaptive consensus control for multiagent systems with dead-zone input and sensor faults. IEEE Transactions on Automation Science and Engineering, 2023, 21(3): 4016−4027 doi: 10.23919/ccc58697.2023.10240204 [97] Holloway J, Krstic M. Prescribed-time observers for linear systems in observer canonical form. IEEE Transactions on Automatic Control, 2019, 64(9): 3905−3912 doi: 10.1109/TAC.2018.2890751 [98] Espitia N, Steeves D, Perruquetti W, Krstic M. Sensor delay-compensated prescribed-time observer for LTI systems. Automatica, 2022, 135: 110005 doi: 10.1016/j.automatica.2021.110005 [99] Zhang J, Zhao X, Zheng G, Zhu F, Dinh T. On distributed prescribed-time unknown input observers. IEEE Transactions on Automatic Control, 2025, 70(7): 4743−4750 doi: 10.1109/TAC.2025.3536856 [100] Holloway J, Krstic M. Prescribed-time output feedback for linear systems in controllable canonical form. Automatica, 2019, 107: 77−85 doi: 10.1016/j.automatica.2019.05.027 [101] Tran D, Yucelen T, Sarsilmaz S B. Finite-time control of multiagent networks as systems with time transformation and separation principle. Control Engineering Practice, 2021, 108: 104717 doi: 10.1016/j.conengprac.2020.104717 [102] Li S, Zhou B, Duan G, Zhang K. Prescribed-time semiglobal output feedback stabilization by a time-varying high-gain observer. Automatica, 2025, 179: 112454 doi: 10.1016/j.automatica.2025.112454 [103] Li S, Zhou B, Shi Y, Duan G. Prescribed-time semi-global control for a class of nonlinear uncertain systems by linear time-varying feedback. IEEE Transactions on Cybernetics, 2025, 55(3): 1172−1182 doi: 10.1109/TCYB.2024.3498838 [104] Vazquez C. Prescribed-time control of disturbed systems with state and input constraints. IEEE Transactions on Automatic Control, 2024, 70(1): 619−626 doi: 10.1109/tac.2024.3438329 [105] Zhang K, Zhou B, Jiang H, Liu G, Duan G. Practical prescribed-time sampled-data control of linear systems with applications to the air-bearing testbed. IEEE Transactions on Industrial Electronics, 2022, 69(6): 6152−6161 doi: 10.1109/TIE.2021.3086720 [106] Efimov D, Orlov Y. Discretization of prescribed-time observers in the presence of noises and perturbations. Systems & Control Letters, 2024, 188: 105820 doi: 10.1016/j.sysconle.2024.105820 [107] Orlov Y, Arambula M, Efimov D. Prescribed-time output feedback for linear systems in normal form: Robustness analysis and digital implementation under measurement noise. Systems & Control Letters, 2026, 209: 106344 doi: 10.1016/j.sysconle.2026.106344 [108] Voleti R, Bhattacharjee D, Subbarao K. Leaderless time-to-go protocols for same-time position consensus. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(6): 3795−3809 doi: 10.1109/TSMC.2023.3234563 [109] Efimov D, Orlov Y. On implicit discretization of prescribed-time stabilizers. In: Proceedings of the 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024: 7350–7355. [110] Efimov D, Orlov Y. On discretization and sampled-time implementation of prescribed-time stabilizing controls. Automatica, 2026, 191: 113106 doi: 10.1016/j.automatica.2026.113106 [111] 成旺磊, 张柯, 姜斌. 基于层级结构的空–地协同预设时间最优容错控制. 自动化学报, 2024, 50(8): 1589−1600 doi: 10.16383/j.aas.c230699 [112] Su J, Song Y. Prescribed-time formation control for multi-agent systems with uncertain nonlinear dynamics and non-vanishing random disturbances. IEEE/CAA Journal of Automatica Sinica, 2026, 13(3): 586−596 doi: 10.1109/JAS.2026.125714 [113] Zhang K, Zhou B, Yang X, Duan G. Prescribed-time leader-following consensus of linear multi-agent systems by bounded linear time-varying protocols. Science China Information Sciences, 2024, 67: 112201 doi: 10.1007/s11432-022-3685-3 [114] Zuo G, Zhu L, Wang Y, Chen Z, Song Y. A novel approach to prescribed-time cooperative output regulation in linear heterogeneous multi-agent systems using cascade system criteria. IEEE Transactions on Circuits and Systems I: Regular Papers, 2025, 72(6): 2842−2855 doi: 10.1109/TCSI.2025.3558826 [115] Ning P, Hua C, Li K, Meng R. Event-triggered control for nonlinear uncertain systems via a prescribed-time approach. IEEE Transactions on Automatic Control, 2023, 68(11): 6975−6981 doi: 10.1109/TAC.2023.3243863 [116] Ning P, Hua C, Li K, Li H. Event-triggered adaptive prescribed-time control for nonlinear systems with uncertain time-varying parameters. Automatica, 2023, 157: 111229 doi: 10.1016/j.automatica.2023.111229 [117] Zhang K, Zhou B, Duan G R. Global consensus of double-integrator multi-agent systems with input saturation by fully distributed event-triggered and self-triggered controls. IEEE Transactions on Automatic Control, 2024, 69(9): 6269−6276 doi: 10.1109/TAC.2024.3374256 [118] Zhang K, Zhou B, Hou M, Duan G R. Practical prescribed-time stabilization of a class of nonlinear systems by event-triggered and self-triggered control. IEEE Transactions on Automatic Control, 2024, 69(5): 3426−3433 doi: 10.1109/TAC.2023.3338749 [119] Zhang K, Hu Z, Song F, Yang X, Liu Y. Consensus of input constrained multi-agent systems by dynamic time-varying event-triggered strategy with a designable minimal inter-event time. IEEE Transactions on Circuits and Systems II: Express Briefs, 2024, 71(4): 2119−2123 [120] Li H, Jia X, Chi X, Li B. Fully distributed prescribed-time leader-following output consensus of heterogeneous multi-agent systems with dynamic event-triggered mechanism. IEEE Transactions on Automation Science and Engineering, 2025, 22: 8341−8350 doi: 10.1109/TASE.2024.3485052 [121] Ye Z, Zhang D, Liu L, Shi Y, Feng G. Prescribed-time consensus of leader-following multi-agent systems under DoS attacks. Automatica, 2026, 188: 112953 doi: 10.1016/j.automatica.2026.112953 [122] Zhang K, Zhou B, Duan G. Fully distributed and attack-immune protocols for prescribed-time consensus by using periodic delayed relative output. IEEE Transactions on Cybernetics, 2026, 56(3): 1379−1389 doi: 10.1109/TCYB.2025.3624549 -
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