Prescribed Error Performance Control for Second-Order Fully Actuated Systems

doi:10.1007/s11424-022-2060-1

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (2): 660-669.DOI: 10.1007/s11424-022-2060-1

Prescribed Error Performance Control for Second-Order Fully Actuated Systems

LI Zhi¹, ZHANG Ying¹, ZHANG Rui²

1. School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China;
2. School of Electronic and Communication Engineering, Shenzhen Polytechnic, Shenzhen 518055, China

Received:2022-01-20 Revised:2022-03-15 Published:2022-04-13
Contact: ZHANG Ying. Email: zhangyinghit@126.com
Supported by:
This paper was supported by the Science Center Program of the National Natural Science Foundation of China under Grant No. 62188101 and the Joint Funds of the National Natural Science Foundation of China under Grant No. U2013203.

PDF ( 9 ) Cited

LI Zhi, ZHANG Ying, ZHANG Rui. Prescribed Error Performance Control for Second-Order Fully Actuated Systems[J]. Journal of Systems Science and Complexity, 2022, 35(2): 660-669.

In this paper, the prescribed error trajectory control is proposed for second-order fully actuated systems. At first, by taking advantage of the full-actuation property, an intermediate control law is designed such that the intermediate closed-loop system is in a very simple form. Then, by utilizing the initial conditions of system states and the prescribed error performance function, the intermediate control law is developed to force the tracking error of the system on the proposed sliding mode surface from the beginning. The overall control law is obtained by combining the aforementioned steps. It is revealed that under the designed control law, the tracking error of the closed-loop system converges to zero along the prescribed error trajectory. Finally, an example is provided to validate the effectiveness of the presented approach.

Key words: Fully actuated systems, prescribed error trajectory, slide mode surface

[1] Jiang B, Hu Q, and Friswell M I, Fixed-time attitude control for rigid spacecraft with actuator saturation and faults, IEEE Transactions on Control Systems Technology, 2016, 24(5): 1892–1898.
[2] Xiao B, Yin S, and Kaynak O, Tracking control of robotic manipulators with uncertain kinematics and dynamics, IEEE Transactions on Industrial Electronics, 2016, 63(10): 6439–6449.
[3] Duan G R, High-order fully actuated system approaches: Part I. Models and basic procedure, International Journal of Systems Science, 2021, 52(2): 422–435.
[4] Duan G R, High-order fully actuated system approaches: Part III. Robust control and high-order backstepping, International Journal of Systems Science, 2021, 52(5): 952–971.
[5] Xia K and Huo W, Robust adaptive backstepping neural networks control for spacecraft rendezvous and docking with uncertainties, ISA Transactions, 2016, 62(3): 249–257.
[6] Shekhar R C, Kearney M, and Shames I, Robust model predictive control of unmanned aerial vehicles using waysets, Journal of Guidance Control Dynamics, 2015, 38(10): 1–10.
[7] Zou A M, Ruiter A, and Kumar K D, Finite-time attitude tracking control for rigid spacecraft with control input constraints, IET Control Theory and Applications, 2017, 11(7): 931–940.
[8] Galicki M, Finite-time trajectory tracking control in a task space of robotic manipulators, Automatica, 2016, 67: 165–170.
[9] Polyakov A, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE Transactions on Automatic Control, 2012, 57(8): 2106–2110.
[10] Sai H Y, Xu Z B, He S, et al., Adaptive nonsingular fixed-time sliding mode control for uncertain robotic manipulators under actuator saturation, ISA Transactions, 2021, DOI: 10.1016/j.isatra.2021.05.011.
[11] Kostarigka A K, Doulgeri Z, and Rovithakis G A, Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity, Automatica, 2013, 49(5): 1137–1147.
[12] Jing C, Xu H, and Niu X, Adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators, ISA Transactions, 2019, 91(2): 41–51.
[13] Boukattaya M, Gassara H, and Damak T, A global time-varying sliding-mode control for the tracking problem of uncertain dynamical systems, ISA Transactions, 2020, 97: 155–170.
[14] Shi X N, Zhou D, Chen X W, et al., Actor-critic-based predefined-time control for spacecraft attitude formation system with guaranteeing prescribed performance on SO(3), Aerospace Science and Technology, 2021, 117: 106898.

[1]	WANG Na, LIU Xiaoping, LIU Cungen, WANG Huanqing, ZHOU Yucheng. Almost Disturbance Decoupling for HOFA Nonlinear Systems with Strict-Feedback Form [J]. Journal of Systems Science and Complexity, 2022, 35(2): 481-501.
[2]	ZHOU Bin, DUAN Guang-Ren. On the Role of Zeros in the Pole Assignment of Scalar High-Order Fully Actuated Linear Systems [J]. Journal of Systems Science and Complexity, 2022, 35(2): 535-542.

Viewed

Full text

Abstract