Abstract: In this article, we present a fixed-time robust attitude control scheme with severe funnel driving constraints for high-speed aircraft developed concerning uncertain signals. First, an adaptive fixed-time radial basis function neural network (AFTR) observer is described, designed as a compensation control based on a converted attitude error system, aiming at eliminating the influence of strong disturbances and uncertainties. Then, we propose a performance-prescribed transformation strategy that can effectively enhance the accuracy of error tracking and state convergence by constructing second-order performance error functions. Based on the above preparation and transformation, we present a double-integral fixed-time sliding mode controller combined with an auxiliary oscillation-suppression function designed to achieve fixed-time convergence of attitude angles and angular rates, which ensures the rapidity of error tracking and state convergence. Finally, the fixed-time stability of the entire closed-loop system is proved via Lyapunov synthesis theory, and the upbound of convergence time is derived. Nominal and comparative simulation cases were used to investigate the effectiveness and reliability of the proposed integrated framework.

高速飞行器固定时间鲁棒姿态跟踪控制：一种精确的漏斗引导方法

[1]AnK, GuoZY, HuangW, et al., 2022. Leap trajectory tracking control based on sliding mode theory for hypersonic gliding vehicle. Journal of Zhejiang University-SCIENCE A, 23(3):188-207.

[2]BaoCY, WangP, TangGJ, 2023. Data-driven based model-free adaptive optimal control method for hypersonic morphing vehicle. IEEE Transactions on Aerospace and Electronic Systems, 59(4):3713-3725.

[3]BechlioulisCP, RovithakisGA, 2008. Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Transactions on Automatic Control, 53(9):2090-2099.

[4]BergerT, RauertAL, 2020. Funnel cruise control. Automatica, 119:109061.

[5]BouaissO, MechgougR, Taleb-AhmedA, et al., 2024. Robust trajectory tracking of quadrotors using adaptive radial basis function network compensation control. Journal of the Franklin Institute, 361(3):1167-1185.

[6]BuXW, 2023. Prescribed performance control approaches, applications and challenges: a comprehensive survey. Asian Journal of Control, 25(1):241-261.

[7]BuXW, XiaoY, 2018. Prescribed performance-based low-computational cost fuzzy control of a hypersonic vehicle using non-affine models. Advances in Mechanical Engineering, 10(2):1-12.

[8]BuXW, HuaCC, LvML, et al., 2023. Flight control of waverider vehicles with fragility-avoidance prescribed performance. IEEE Transactions on Aerospace and Electronic Systems, 59(5):5248-5261.

[9]ChenHL, WangP, TangGJ, 2023. Fuzzy disturbance observer-based fixed-time sliding mode control for hypersonic morphing vehicles with uncertainties. IEEE Transactions on Aerospace and Electronic Systems, 59(4):3521-3530.

[10]ChenLL, LiuZB, DangQQ, et al., 2024. Robust fixed-time flight controller for a dual-system convertible UAV in the cruise mode. Defence Technology, 39:53-66.

[11]ChenM, WangHQ, LiuXP, 2021. Adaptive fuzzy practical fixed-time tracking control of nonlinear systems. IEEE Transactions on Fuzzy Systems, 29(3):664-673.

[12]DingYB, YueXK, LiuC, et al., 2022. Finite-time controller design with adaptive fixed-time anti-saturation compensator for hypersonic vehicle. ISA Transactions, 122:96-113.

[13]DongZH, LiYH, LvML, et al., 2022. Fuzzy adaptive prescribed performance fault-tolerant control for HFVs with fixed-time convergence guarantee. International Journal of Aerospace Engineering, 2022:2438657.

[14]GuoYY, XuB, 2022. Finite-time deterministic learning command filtered control for hypersonic flight vehicle. IEEE Transactions on Aerospace and Electronic Systems, 58(5):4214-4225.

[15]KeshmiriS, MirmiraniM, ColgrenR, 2012. Six-DOF modeling and simulation of a generic hypersonic vehicle for conceptual design studies. AIAA Modeling and Simulation Technologies Conference and Exhibit, p.1-12.

[16]LiCY, WangW, LiuZJ, et al., 2024. Adaptive neural network based fixed-time attitude tracking control of spacecraft considering input saturation. Aerospace Science and Technology, 155:109746.

[17]LiWT, ZhaoJS, SuSW, et al., 2023. Adaptive output feedback attitude control for reusable launch vehicle with input constraints and actuator faults. Aerospace Science and Technology, 142:108616.

[18]LiuSH, YanJG, CaoJF, et al., 2021. Review of the precise orbit determination for Chinese lunar exploration projects. Earth and Space Science, 8(4):e2020EA001361.

[19]LunYB, WangHL, WuTC, et al., 2024. A changeable boundary prescribed performance control for the altitude ground test facility. Nonlinear Dynamics, 112(6):4483-4506.

[20]MengY, YuX, ZhuYK, et al., 2024. Fixed-time attitude control of reusable launch vehicles utilizing reliability-based control allocation. Control Engineering Practice, 151:106013.

[21]MoulayE, LéchappéV, BernuauE, et al., 2022. Fixed-time sliding mode control with mismatched disturbances. Automatica, 136:110009.

[22]ParsegovS, PolyakovA, ShcherbakovP, 2012. Nonlinear fixed-time control protocol for uniform allocation of agents on a segment. The 51st IEEE Conference on Decision and Control, p.7732-7737.

[23]PolyakovA, 2012. Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control, 57(8):2106-2110.

[24]QianCJ, LinW, 2001. Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Systems & Control Letters, 42(3):185-200.

[25]ShenYX, ZhouDJ, WuYD, et al., 2023. Anti-disturbance control for HVs system subject to nonlinear actuator characteristics with extended state observer. Journal of the Franklin Institute, 360(18):14676-14695.

[26]SongJG, ZhangJX, 2024. Fault-tolerant prescribed performance control of nonlinear systems with process faults and actuator failures. ISA Transactions, 144:220-227.

[27]SunJL, YiJQ, PuZQ, et al., 2020. Fixed-time sliding mode disturbance observer-based nonsmooth backstepping control for hypersonic vehicles. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(11):4377-4386.

[28]TanJ, GuoSJ, 2022. Backstepping control with fixed-time prescribed performance for fixed wing UAV under model uncertainties and external disturbances. International Journal of Control, 95(4):934-951.

[29]WangF, ZhouC, HuaCC, 2024. Adaptive predefined time neural filtered control design for an uncertain nonlinear system and application to flight control. Applied Mathematical Modelling, 129:25-47.

[30]WangG, XiaHW, 2024. Fault-tolerant learning control of air-breathing hypersonic vehicles with uncertain parameters and actuator faults. Expert Systems with Applications, 238:121874.

[31]WangYY, HuJB, 2018. Improved prescribed performance control for air-breathing hypersonic vehicles with unknown deadzone input nonlinearity. ISA Transactions, 79:95-107.

[32]WuTC, WangHL, YuY, et al., 2021. Quantized fixed-time fault-tolerant attitude control for hypersonic reentry vehicles. Applied Mathematical Modelling, 98:143-160.

[33]WuYJ, ShaoKJ, WangN, et al., 2023. Finite-time path following control of a sailboat with actuator failure and unknown sideslip angle. Journal of Zhejiang University-SCIENCE A, 24(9):749-761.

[34]XinB, ChengS, WangQ, et al., 2023. Fixed-time prescribed performance consensus control for multiagent systems with non-affine faults. IEEE Transactions on Fuzzy Systems, 31(10):3433-3446.

[35]XuSH, GuanYZ, WeiCZ, et al., 2022. Reinforcement-learning-based tracking control with fixed-time prescribed performance for reusable launch vehicle under input constraints. Applied Sciences, 12(15):7436.

[36]YinZY, WangB, XiongRT, et al., 2024. Attitude tracking control of hypersonic vehicle based on an improved prescribed performance dynamic surface control. The Aeronautical Journal, 128(1323):875-895.

[37]ZhangBC, LiangYY, RaoST, et al., 2024. RBFNN-based anti-input saturation control for hypersonic vehicles. Aerospace, 11(2):108.

[38]ZhangH, WangP, TangGJ, et al., 2023. Fixed-time sliding mode control for hypersonic morphing vehicles via event-triggering mechanism. Aerospace Science and Technology, 140:108458.

[39]ZhangH, WangP, TangG, et al., 2024. Disturbance observer-based fixed-time control for hypersonic morphing vehicles with uncertainties. The Aeronautical Journal, 128(1326):1844-1874.

[40]ZhaoHW, YangLB, 2022. Global adaptive neural backstepping control of a flexible hypersonic vehicle with disturbance estimation. Aircraft Engineering and Aerospace Technology: An International Journal, 94(4):492-504.

[41]ZhaoJQ, FengDZ, CuiJS, et al., 2022. Finite-time extended state observer-based fixed-time attitude control for hypersonic vehicles. Mathematics, 10(17):3162.

[42]ZhaoSW, WangJC, XuHT, et al., 2023a. ADP-based attitude-tracking control with prescribed performance for hypersonic vehicles. IEEE Transactions on Aerospace and Electronic Systems, 59(5):6419-6431.

[43]ZhaoSW, WangJC, XuHT, et al., 2023b. Composite observer-based optimal attitude-tracking control with reinforcement learning for hypersonic vehicles. IEEE Transactions on Cybernetics, 53(2):913-926.

[44]ZuoZY, 2015. Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica, 54:305-309.

[45]ZuoZY, TieL, 2014. A new class of finite-time nonlinear consensus protocols for multi-agent systems. International Journal of Control, 87(2):363-370.