A Novel Approach to Fixed-Time Stabilization for a Class of Uncertain Second-Order Nonlinear Systems
Source abstract
Abstract
This paper is concerned with the problem of fixed-time stabilization for a class of uncertain second-order nonlinear systems. By delicately introducing extra manipulations in the feedback domination and revamping the technique of adding a power integrator, a new approach is developed, by which a state feedback controller, together with a suitable Lyapunov function, which is critical for verifying fixed-time convergence, can be explicitly organized to render the closed-loop system fixed-time stable. The major novelty of this paper is attributed to a subtle strategy that offers a distinct perspective in controller design as well as stability analysis in the problem of fixed-time stabilization for nonlinear systems. Finally, the proposed approach is applied to the attitude stabilization of a spacecraft to demonstrate its merits and effectiveness.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Adaptive Control of Nonlinear Systems · Guidance and Control Systems · Stability and Control of Uncertain Systems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan 70101, Taiwan
References (45)
Show source-provided references
1. Krstic, M., Kanellakopoulos, I., and Kokotovic, P.V. (1995). Nonlinear and Adaptive Control Design, John Wiley.
2. Isidori, A. (1995). Nonlinear Control Systems, Springer. [3rd ed.].10.1007/978-1-84628-615-5 ↗
3. A new second-order sliding mode and its application to nonlinear constrained systems10.1109/TAC.2018.2867163 ↗
4. Stable adaptive fuzzy control of nonlinear systems10.1109/91.227383 ↗
5. Finite-time analysis and H∞ control for switched stochastic systems10.1016/j.jfranklin.2011.10.021 ↗
6. Nonsmooth stabilization of a class of nonlinear cascaded systems10.1016/j.automatica.2012.06.060 ↗
7. Global sampled-data output feedback stabilization for a class of uncertain nonlinear systems10.1016/j.automatica.2018.11.002 ↗
8. Cheng, Y., Zhang, J., Du, H., Wen, G., and Lin, X. (2019). Global event-triggered output feedback stabilization of a class of nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst., in press.
9. Finite-time stability of continuous autonomous systems10.1137/S0363012997321358 ↗
10. Finite time stability conditions for non-autonomous continuous system10.1080/00207170701650303 ↗
11. Global finite-time stabilization via time-varying feedback for uncertain nonlinear systems10.1137/130920423 ↗
12. A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system10.1016/j.automatica.2015.05.005 ↗
13. Finite-time stabilization for a class of high-order stochastic nonlinear systems with an output constraint
14. Global finite-time stabilisation for a class of nonlinear systems10.1080/00207721003770569 ↗
15. Finite-time stabilisation of a class of switched nonlinear systems with state constraints10.1080/00207179.2017.1314018 ↗
16. Chen, C.C., and Sun, Z.Y. (2019). A unified approach to finite-time stabilization of high-order nonlinear systems with an asymmetric output constraint. Automatica, in press.10.1016/j.automatica.2019.108581 ↗
17. Wu, D., Du, H., Wen, G., and Lü, J. (2019). Fixed-time synchronization control for a class of master-slave systems based on homogeneous method. IEEE Trans. Circuits Syst. II Express Briefs, in press.10.1109/TCSII.2018.2886574 ↗
18. A unified approach to finite-time stabilization of high-order nonlinear systems with and without an output constraint10.1002/rnc.4393 ↗
19. Global finite-time control for a class of switched nonlinear systems with different powers via output feedback10.1080/00207721.2018.1512679 ↗
20. A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators10.1109/9.362847 ↗
21. Non-singular terminal sliding mode control of rigid manipulators10.1016/S0005-1098(02)00147-4 ↗
22. Study of nonsingular fast terminal sliding-mode fault-tolerant control
23. Nonlinear feedback design for fixed-time stabilization of linear control systems10.1109/TAC.2011.2179869 ↗
24. Fixed-time stabilisation for a class of high-order nonlinear systems10.1049/iet-cta.2018.5053 ↗
25. Uniform robust exact differentiator10.1109/TAC.2011.2160030 ↗
26. Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application10.1016/j.nahs.2018.08.005 ↗
27. Continuous finite- and fixed-time high-order regulators10.1016/j.jfranklin.2016.09.026 ↗
28. Nonsingular fixed-time consensus tracking for second-order multi-agent networks10.1016/j.automatica.2015.01.021 ↗
29. An overview of recent advances in fixed-time cooperative control of multiagent systems10.1109/TII.2018.2817248 ↗
30. Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system
31. Multivariable continuous fixed-time secondorder sliding mode control: design and convergence time estimation10.1049/iet-cta.2016.0572 ↗
32. Robust stabilization of MIMO systems in finite/fixed time10.1002/rnc.3297 ↗
33. Fixed-time attitude control for rigid spacecraft with actuator saturation and faults10.1109/TCST.2016.2519838 ↗
34. A continuous feedback approach to global strong stabilization of nonlinear systems10.1109/9.935058 ↗
35. Study of nonlinear integral sliding mode fault-tolerant control10.1109/TMECH.2015.2474700 ↗
36. Xiao, B., Yang, X., Karimi, H.K., and Qiu, J. (2019). Asymptotic tracking control for a more representative class of uncertain nonlinear systems with mismatched uncertainties. IEEE Trans. Ind. Electron., in press.10.1109/TIE.2019.2893852 ↗
37. Pan, Y., Li, X., and Yu, H. (2019). Efficient PID tracking control of robotic manipulators driven by compliant actuators. IEEE Trans. Control. Syst. Technol.10.1109/TCST.2017.2783339 ↗
38. Filippov, A.F. (1988). Differential Equations with Discontinuous Righthand Sides, Kluwer Academic Publishers.10.1007/978-94-015-7793-9 ↗
39. Finite time stability and robust control synthesis of uncertain switched systems10.1137/S0363012903425593 ↗
40. Chen, C.C., and Sun, Z.Y. (2019). A new approach to stabilisation of a class of nonlinear systems with an output constraint. Int. J. Control., in press.
41. Hardy, G., Littlewood, J., and Polya, G. (1988). Inequalities, Cambridge University Press.
42. Royden, H.L., and Fitzpatrik, P.M. (2010). Real Analysis, Pearson. [4th ed.].
43. Bacciotti, A., and Rosier, L. (2005). Liapunov Functions and Stability in Control Theory, Springer. [2nd ed.].10.1007/b139028 ↗
44. Chobotov, V.A. (1991). Spacecraft Attitude Dynamics and Control, Krieger.
45. Zoriach, V.A. (2016). Mathematical Analysis II, Springer.10.1007/978-3-662-48993-2 ↗