RISE-Based Asymptotic Prescribed Performance Tracking Control of Nonlinear Servo Mechanisms
Abstract
Most function approximator (e.g., neural network or fuzzy system) based control designs can only prove uniform ultimate boundedness of the controlled system due to the unavoidable approximation errors. Moreover, the transient response of conventional adaptive control may be sluggish because high-gain learning is not preferable for guaranteeing system safety. To address these issues, this paper proposes and experimentally validates an alternative robust adaptive control for servo mechanisms with unknown dynamics and bounded disturbances. This control can guarantee asymptotic tracking error convergence in the steady-state, while the transient response can also be prescribed by using an improved prescribed performance function. An echo state network augmented by a smooth friction model is used to accommodate the unknown nonlinearities. The residual approximation error and other bounded disturbances are compensated by using a robust integral of sign of the error term. Comparative experiments based on a practical turntable servo mechanism are conducted to validate the effectiveness of the proposed control scheme and show improved control performance.
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RISE/ARISE control greatly improves the trajectory tracking accuracy of electro-hydraulic servo systems.
“The above literature shows that RISE/ARISE control greatly improves the trajectory tracking accuracy of EHSS.”
From RISE-based adaptive control of electro-hydraulic servo system with uncertain compensation (2023) · cites this paper as [20]
The RISE controller guarantees asymptotic tracking performance owing to the strong robustness of its integral robust control law against smooth time-varying disturbances.
“The robust integral of the sign of the error (RISE) controller [10,11] guarantees asymptotic tracking performance owing to the strong robustness of its integral robust control law against smooth time-varying disturbances.”
From Predefined-Time Tracking Control of Servo Hydraulic Cylinder Based on Reinforcement Learning (2025) · cites this paper as [10]
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“Second, unlike the reported NN techniques [1]–[3], [25], [32], the ESN-MLP neural observer avoids the notorious difficulty of time-consuming online learning by regulating the maximum norm instead of directly using the components of neural weight vectors.”
BackgroundResultInfluentialDing, R., Ding, C., Xu, Y., Liu, W., & Yang, X. (2021) · ISA Transactions · doi:10.1016/j.isatra.2021.12.026 · Cited by 29 · see citing works
Wang, Y., Wu, G., & Wang, Y. (2023) · Fuel · doi:10.1016/j.fuel.2023.129019 · Cited by 28 · see citing works
Adaptive prescribed performance control for hydraulic system with disturbance compensation
Xu, Z., Liu, Q., & Yao, J. (2021) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3262 · Cited by 28 · see citing works
“is bounded by Vb(t) ≤ exp(−λt)Vb(0) + σ λ [1 − exp(−λt)], (30)”
Yang, X., Ge, Y., Deng, W., & Yao, J. (2022) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2022.02.008 · Cited by 27 · see citing works
Output feedback adaptive RISE control for uncertain nonlinear systems
Yang, G., Zhu, T., Yang, F., Cui, L., & Wang, H. (2022) · Asian Journal of Control · doi:10.1002/asjc.2793 · Cited by 26 · see citing works
“Assumption 1 is common for RISE-based controller design and meanwhile has been verified to be reasonable by many experiments in [19, 20, 23].”
BackgroundChen, Q., Jin, Y., & Song, Y. (2021) · Neurocomputing · doi:10.1016/j.neucom.2021.10.083 · Cited by 25 · see citing works
Chen, Z., Chen, Q., He, X., & Sun, M. (2018) · IEEE Access · doi:10.1109/access.2018.2875971 · Cited by 24 · see citing works
Constrained Attitude Control of Uncertain Spacecraft With Appointed-Time Control Performance
Lu, X., Jia, Y., Fu, Y., & Matsuno, F. (2022) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2022.3174845 · Cited by 22 · see citing works
“performance control method [48]–[50] has been proposed, where the prescribed performance control problem of the original control system is converted into the stabilization problem of an unconstrained nonlinear control system.”
MethodEvent-Triggered Prespecified Performance Control for Steer-by-Wire Systems With Input Nonlinearity
Wang, Y.-F., Ma, B., Wang, D.-H., & Chai, T.-Y. (2023) · IEEE transactions on intelligent transportation systems (Print) · doi:10.1109/tits.2023.3242949 · Cited by 21 · see citing works
“…performance controller proposed in [18], [19], [20], [21], [22], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], and [39], a priori bounds of the initial state errors is no longer required in the control design and the tracking error of SbW systems…”
BackgroundMethodInfluentialZhang, M., Huang, J., Cao, Y., Xiong, C., & Mohammed, S. (2022) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2022.3172715 · Cited by 23 · see citing works
“Although the potential of ESN to approximate model uncertainties has been proved by the applications on the dc motor [23] and servo mechanism [24], ESN are rarely found in the field of assistive robotics.”
BackgroundChen, Q., Li, X., Zhang, A., & Song, Y. (2022) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2022.3189189 · Cited by 23 · see citing works
“Different from LSMs built upon spiking neurons that are more complex and have not been widely used in control schemes, ESNs are based on analog sigmoidal neurons and have been successfully applied in dynamic system identification or control [24]–[31].”
MethodFractional-Order Echo State Network Backstepping Control of Fractional-Order Nonlinear Systems
Liu, H., Shi, J., Cao, J., & Pan, Y. (2023) · IEEE Transactions on Emerging Topics in Computational Intelligence · doi:10.1109/tetci.2023.3309739 · Cited by 23 · see citing works
“Wang et al. [37] put forward an ESN extended by a smooth friction model to design a robust adaptive control method.”
MethodFinite-time command-filtered approximation-free attitude tracking control of rigid spacecraft
Xie, S., Chen, Q., He, X., Tao, M., & Tao, L. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-021-07091-x · Cited by 22 · see citing works
Yuan, S., Deng, W., Liang, X., Yao, J., & Yang, G. (2023) · ISA Transactions · doi:10.1016/j.isatra.2023.02.002 · Cited by 22 · see citing works
Zhang, G., Li, Z., Li, J., Zhang, W., & Qiu, B. (2025) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2025.3562245 · Cited by 21 · see citing works
Approximate Optimal Stabilization Control of Servo Mechanisms based on Reinforcement Learning Scheme
Lv, Y., Ren, X., Hu, S., & Xu, H. (2019) · International Journal of Control Automation and Systems · doi:10.1007/s12555-018-0551-6 · Cited by 21 · see citing works
Self-citationWang, C., Li, D.-H., Zhang, H., Ma, P., Li, X., Zhang, S., & Dong, Y. (2023) · Applied Energy · doi:10.1016/j.apenergy.2023.122414 · Cited by 19 · see citing works
Finite time parameter estimation-based adaptive predefined performance control for servo mechanisms
Wang, S., Na, J., Yu, H., & Chen, Q. (2018) · ISA Transactions · doi:10.1016/j.isatra.2018.11.029 · Cited by 18 · see citing works
Self-citationGao, X., Sun, B., Hu, X., & Zhu, K. (2020) · Mathematical Problems in Engineering · doi:10.1155/2020/2534038 · Cited by 18 · see citing works
Wang, S., Ding, J., & Ji, Y. (2024) · IEEE Transactions on Transportation Electrification · doi:10.1109/tte.2024.3374273 · Cited by 18 · see citing works
Self-citationDing, R., Ding, C., Xu, Y., & Yang, X. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-022-07258-0 · Cited by 18 · see citing works
“For instance, the digital signal processing board based control platform in [27].”
BackgroundMethodTao, L., Chen, Q., Nan, Y., Dong, F., & Jin, Y. (2018) · Complexity · doi:10.1155/2018/5632939 · Cited by 18 · see citing works
“The demands of control systems with large inertia and high power load are increasing in modern engineering systems [1].”
BackgroundMatsubara, T., Miyatake, Y., & Yaguchi, T. (2023) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2023.3242345 · Cited by 22 · see citing works
“To handle the nonlinearity, fractional order methods and fuzzy logic systems (FLSs) have been proposed to model dynamical systems [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20].”
MethodContinuous Integral Robust Control of Electro-Hydraulic Systems With Modeling Uncertainties
Ma, W., Deng, W., & Yao, J. (2018) · IEEE Access · doi:10.1109/access.2018.2866270 · Cited by 17 · see citing works
“It has been successfully employed to cope with the tracking control problem of motor servo systems [22], [23] quadrotor unmanned aerial vehicle (UAV) [24], helicopter [25], as well as friction identification issue of Euler-Lagrange system [26].”
MethodWei, C., Liao, Y., Xi, W., Yin, Z., & Luo, J. (2020) · Journal of Vibration and Control · doi:10.1177/1077546320902562 · Cited by 16 · see citing works
RISE-based prescribed performance control of Euler–Lagrange systems
Asl, H. J., Narikiyo, T., & Kawanishi, M. (2019) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2019.06.033 · Cited by 15 · see citing works
Cao, L., Huang, X., Ye, H., & Song, Y. (2023) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2022.3232699 · Cited by 15 · see citing works
“Here, in this work, we consider a class of MIMO nonlinear systems with mismatched nonlinearities and nonvanishing external disturbances as well as actuation saturation, which is more general and difficult to deal with compared with existing study [15], [34], [35], [36].”
Wang, H., Shao, X., Li, J., & Liu, J. (2019) · Aerospace Science and Technology · doi:10.1016/j.ast.2019.06.029 · Cited by 15 · see citing works
Neural-Adaptive Constrained Flight Control for Air–Ground Recovery Under Terrain Obstacles
Su, Z., Wang, X., & Wang, H. (2021) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2021.3101592 · Cited by 14 · see citing works
Fractional order inspired iterative adaptive control
Varga, B., Tar, J. K., & Horváth, R. (2023) · Robotica · doi:10.1017/s0263574723001595 · Cited by 14 · see citing works
“[58], prescribed performance controller (PPC) was introduced and experimentally verified, where asymptotic error convergence was achieved through RISE-based (robust integral of sign of error) control design.”
MethodYang, S., Pang, H., Liu, L., Zheng, L., Wang, L., & Liu, M. (2024) · Nonlinear Dynamics · doi:10.1007/s11071-024-09569-w · Cited by 14 · see citing works
“Especially, when the control input involves the online adaptive process noise, the potential overshoot and lagging response could lead to the TCP degeneration for the control system [17].”
Adaptive Neural Funnel Control for Nonlinear Two-Inertia Servo Mechanisms With Backlash
Wang, S., Yu, H., Yu, J., & Gao, X. (2019) · IEEE Access · doi:10.1109/access.2019.2898925 · Cited by 14 · see citing works
Self-citationXu, G., Xia, Y., Zhai, D., & Lyu, W. (2022) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3484 · Cited by 12 · see citing works
“?̇?i + ( αi − ri εi ) εi + βisig(εi)γi = 0, (28)”
BackgroundData learning‐based model‐free adaptive control and application to an NAO robot
Liu, S., Li, Z., Ji, H., Hou, Z., & Chen, L. (2022) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.6537 · Cited by 12 · see citing works
“13,14 In addition, when the robot is moving, large amounts of data can be collected and processed online due to the development of hardware and computer processing abilities.”
BackgroundChen, Z., Luo, S., Yu, Y., Wang, K., & Ouakad, H. M. (2024) · ISA Transactions · doi:10.1016/j.isatra.2024.06.008 · Cited by 11 · see citing works
Ming, C., & Wang, X. (2020) · International Journal of Aerospace Engineering · doi:10.1155/2020/1676739 · Cited by 10 · see citing works
“Owing to the significant advantages in improving the control performance, the PPC is introduced to the vehicle suspension system [33], manipulator system [34], servo mechanisms [35, 36], unmanned aerial vehicle [37], spacecraft [38–40], etc.”
BackgroundFaraji, A., Sadrossadat, S. A., Yazdian‐Dehkordi, M., Nabavi, M., & Savaria, Y. (2022) · IEEE Access · doi:10.1109/access.2022.3226323 · Cited by 10 · see citing works
“INTRODUCTION With the increasing complexity of systems exploiting nonlinear circuits and components, control and macromodeling them with high accuracy remains an important concern and active research area [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12].”
BackgroundAdaptive Barrier Control for Nonlinear Servomechanisms with Friction Compensation
Wang, S., Yu, H., Gao, X., & Wang, N. (2018) · Complexity · doi:10.1155/2018/8925838 · Cited by 10 · see citing works
“For example, an adaptive prescribed performance tracking control was developed for servomechanisms to achieve position tracking [28].”
Self-citationBackstepping Control Strategy of an Autonomous Underwater Vehicle Based on Probability Gain
Peng, Y., Guo, L., & Meng, Q. (2022) · Mathematics · doi:10.3390/math10213958 · Cited by 10 · see citing works
Constrained docking control for shipborne UAV SideArm recovery
Su, Z., Xing, Z., Xuebing, L. I., Li, C., Wang, X., & Wang, H. (2023) · Chinese Journal of Aeronautics · doi:10.1016/j.cja.2023.12.016 · Cited by 10 · see citing works
RISE-based adaptive control of electro-hydraulic servo system with uncertain compensation
Yang, X., Cui, Y., Yuan, Z., & Hang, J. (2023) · Mathematical Biosciences and Engineering · doi:10.3934/mbe.2023407 · Cited by 9 · see citing works
Wang, X., & Wang, S. (2024) · IEEE Journal of Emerging and Selected Topics in Industrial Electronics · doi:10.1109/jestie.2024.3417375 · Cited by 9 · see citing works
“In addition, the smooth bounded disturbance systems have successfully utilized the robust integral of the sign of the error (RISE) to compensate for the disturbance observation errors of ESO [29], [30].”
Self-citationLv, Y., Zhang, W., Jian, L., & Chang, H. (2026) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2026.114276 · Cited by 9 · see citing works
Zhao, J., Huang, Y., & Zang, W. (2023) · Asian Journal of Control · doi:10.1002/asjc.3121 · Cited by 9 · see citing works
“From [35, 36], we will transform the condition (15) into an equivalent “unconstrained” one.”
MethodAdaptive Neural Control for Hysteresis Motor Driving Servo System with Bouc‐Wen Model
Gao, X. (2018) · Complexity · doi:10.1155/2018/9765861 · Cited by 9 · see citing works
RISE-Adaptive Neural Control for Robotic Manipulators With Unknown Disturbances
Shao, S., & Zhang, K. (2020) · IEEE Access · doi:10.1109/access.2020.2997383 · Cited by 9 · see citing works
Wang, B., Cai, Y., Song, J., & Sepehri, N. (2024) · Transactions of the Institute of Measurement and Control · doi:10.1177/01423312231201676 · Cited by 8 · see citing works
“The RISE control can obtain asymptotic tracking performance with a continuous control law, and its effectiveness has been validated in mechanical servosystems (Ding et al., 2021; Wang et al., 2018; Yao et al., 2014).”
BackgroundXu, S., Guan, Y., Wei, C., & Xu, H. (2025) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2024.109962 · Cited by 8 · see citing works
Cong, S., Wang, D., Liu, L., Li, T., & Peng, Z. (2023) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2023.3305969 · Cited by 8 · see citing works
“As powerful approximation techniques, neural networks (NNs) and fuzzy logic system (FLS) are capable of approximating continuous nonlinear functions [31], with widely applications [32], [33], [34], [35], [36], [37].”
BackgroundNeuroadaptive Robust Speed Control for PMSM Servo Drives with Rotor Failure
Aguilar-Mejía, O., Minor-Popocatl, H., Pacheco-Garcia, P. F., & Tapia-Olvera, R. (2021) · Applied Sciences · doi:10.3390/app112311090 · Cited by 8 · see citing works
“The friction model has been used in [22,23] to describe the compensation of the unknown frictions.”
MethodGao, S., Dong, H., & Zheng, W. (2019) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.4713 · Cited by 8 · see citing works
Adaptive Predefined Performance Neural Control for Robotic Manipulators with Unknown Dead Zone
Shao, S., Zhang, K., Li, J., & Wang, J. (2020) · Mathematical Problems in Engineering · doi:10.1155/2020/6490167 · Cited by 8 · see citing works
Liang, H., Yu, J., & Li, H. (2025) · Ocean Engineering · doi:10.1016/j.oceaneng.2025.120436 · Cited by 7 · see citing works
Kim, B. M., & Yoo, S. J. (2022) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.6351 · Cited by 7 · see citing works
“( − 1 f a,i z⊤a,iFa,iza,i + f a,i f a,i ) ||Ψa,i||(2)θa,i ≤ f a,i ?́?||Ψa,i||(2)θa,i f a,i(z⊤a,iza,i + ?́?) , (22)”
- Authors
- Wang, S., Na, J., & Ren, X.
- Affiliations
- Beijing Institute of Technology (CN)
- Kunming University of Science and Technology (CN)
- Venue
- IEEE Transactions on Systems, Man, and Cybernetics: Systems
- Published
- 2018-12
- Volume
- 48
- Issue
- 12
- Pages
- 2359-2370
- ISSN
- 2168-2216 (ISSN-L)
- 2168-2232
- OpenAlex
- W2770970225
- Cited by
- 159
- References
- 55
- Citations by year
- 2026: 2 · 2025: 11 · 2024: 22 · 2023: 24 · 2022: 24 · 2021: 16 · 2020: 12 · 2019: 29 · 2018: 19
- FWCI
- 10.31
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Systems Man and Cybernetics Systems (publishedVersion)
- Funders
- National Natural Science Foundation of China (61433003, 61573174)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Iterative Learning Control Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Keywords
- prescribed performance control, asymptotic tracking, robust adaptive control, echo state networks, bounded disturbances, transient response, unknown dynamics
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