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A framework for prescribed-time control design via time-scale transformation

Shakouri, A ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1109/LCSYS.2021.3136757
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2021
  4. Abstract:
  5. This letter presents a unified framework for the design of prescribed-time controllers under time-varying input and state constraints for normal-form unknown nonlinear systems with uncertain input gain. The proposed approach is based on a time-domain mapping method by which any infinite-time system can be corresponded to a prescribed-time system and vice versa. It is shown that the design of a constrained nonasymptotic prescribed-time controller can be reduced to the asymptotic control design for an associated constrained infinite-time system. Faà di Bruno’s formula and Bell polynomials are used for a constructive representation of the associated infinite-time system. The presented results are not confined to a particular mapping function, which adds to the flexibility of the proposed scheme. It is shown that necessary and sufficient conditions on the uniform (practical) prescribed-time stability and attractivity can be obtained as corollaries of the main result. IEEE
  6. Keywords:
  7. Bells ; Controllers ; Mapping ; Mathematical transformations ; Polynomials ; Robustness (control systems) ; Time domain analysis ; Time varying control systems ; Bell polynomial ; Bell polynomials ; Control design ; Convergence ; Di bruno’ ; Faà ; FAA ; Prescribed-time control ; Robustness ; S formula ; State and input constraints ; Time control ; Time-transformation mapping ; Time-varying systems ; Transformation mapping ; Uncertainty ; Nonlinear systems
  8. Source: IEEE Control Systems Letters ; 2021 ; 24751456 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/9656547