Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers
This paper is concerned with the tracking control problem for the lower-triangular systems with unknown fractional powers and nonparametric uncertainties. A prescribed performance control approach is put forward as a means of resolving this problem. The proposed control law incorporates a set of bar...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/8/594 |
| _version_ | 1797584689753489408 |
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| author | Kai-Di Xu Jin-Xi Zhang |
| author_facet | Kai-Di Xu Jin-Xi Zhang |
| author_sort | Kai-Di Xu |
| collection | DOAJ |
| description | This paper is concerned with the tracking control problem for the lower-triangular systems with unknown fractional powers and nonparametric uncertainties. A prescribed performance control approach is put forward as a means of resolving this problem. The proposed control law incorporates a set of barrier functions to guarantee error constraints. Unlike the previous works, our approach works for the cases where the fractional powers, the nonlinearities, and their bounding functions or bounds are totally unknown; no restrictive conditions on the powers, such as power order restriction, specific size limitation or homogeneous condition, are made. Moreover, neither the powers and system nonlinearities nor their bounding functions or bounds are needed. It achieves reference tracking with the preassigned tracking accuracy and convergence speed. In addition, our controller is simple, as it does not necessitate parameter identification, function approximation, derivative calculation, or adding a power integrator technique. At the end, a comparative simulation demonstrates the effectiveness and advantage of the proposed approach. |
| first_indexed | 2024-03-10T23:55:19Z |
| format | Article |
| id | doaj.art-66e6c6d41c04471d95d3d9531490e3d8 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T23:55:19Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-66e6c6d41c04471d95d3d9531490e3d82023-11-19T01:11:13ZengMDPI AGFractal and Fractional2504-31102023-08-017859410.3390/fractalfract7080594Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional PowersKai-Di Xu0Jin-Xi Zhang1State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, ChinaState Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, ChinaThis paper is concerned with the tracking control problem for the lower-triangular systems with unknown fractional powers and nonparametric uncertainties. A prescribed performance control approach is put forward as a means of resolving this problem. The proposed control law incorporates a set of barrier functions to guarantee error constraints. Unlike the previous works, our approach works for the cases where the fractional powers, the nonlinearities, and their bounding functions or bounds are totally unknown; no restrictive conditions on the powers, such as power order restriction, specific size limitation or homogeneous condition, are made. Moreover, neither the powers and system nonlinearities nor their bounding functions or bounds are needed. It achieves reference tracking with the preassigned tracking accuracy and convergence speed. In addition, our controller is simple, as it does not necessitate parameter identification, function approximation, derivative calculation, or adding a power integrator technique. At the end, a comparative simulation demonstrates the effectiveness and advantage of the proposed approach.https://www.mdpi.com/2504-3110/7/8/594fractional powerslower-triangular systemsnonparametric uncertaintiesprescribed performancereference tracking |
| spellingShingle | Kai-Di Xu Jin-Xi Zhang Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers Fractal and Fractional fractional powers lower-triangular systems nonparametric uncertainties prescribed performance reference tracking |
| title | Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers |
| title_full | Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers |
| title_fullStr | Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers |
| title_full_unstemmed | Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers |
| title_short | Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers |
| title_sort | prescribed performance tracking control of lower triangular systems with unknown fractional powers |
| topic | fractional powers lower-triangular systems nonparametric uncertainties prescribed performance reference tracking |
| url | https://www.mdpi.com/2504-3110/7/8/594 |
| work_keys_str_mv | AT kaidixu prescribedperformancetrackingcontroloflowertriangularsystemswithunknownfractionalpowers AT jinxizhang prescribedperformancetrackingcontroloflowertriangularsystemswithunknownfractionalpowers |