Abstract
While non-smooth approaches (including sliding mode control) provide explicit feedback laws that ensure finite-time stabilization but in terminal time that depends on the initial condition, fixed-time optimal control with a terminal constraint ensures regulation in prescribed time but lacks the explicit character in the presence of nonlinearities and uncertainties. In this paper we present an alternative to these approaches, which, while lacking optimality, provides explicit time-varying feedback laws that achieve regulation in prescribed finite time, even in the presence of non-vanishing (though matched) uncertain nonlinearities. Our approach employs a scaling of the state by a function of time that grows unbounded towards the terminal time and is followed by a design of a controller that stabilizes the system in the scaled state representation, yielding regulation in prescribed finite time for the original state.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 3837-3842 |
| Number of pages | 6 |
| ISBN (Electronic) | 9781509018376 |
| DOIs | |
| Publication status | Published - Dec 2016 |
| Externally published | Yes |
Funding
This work was supported in part by the Major State Basic Research Development Program 973 (No. 2012CB215202), and the National Natural Science Foundation of China (No.61134001).
Keywords
- fixed-time stabilization
- input-to-state stability
- Nonlinear control
- small-gain theorem