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Prescribed performance-barrier Lyapunov function for the adaptive control of unknown pure-feedback systems with full-state constraints

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Abstract

In this paper, an adaptive state-feedback control technique is proposed for a class of unknown pure-feedback systems. A remarkable feature is that not only the problem of full-state constraints and prescribed performance tracking is solved together, but also the design is an approximation-free control scheme for pure-feedback systems with completely unknown nonlinearities. These properties will lead to a difficult task for designing a stable controller. To this end, a novel prescribed performance-barrier Lyapunov function is developed to guarantee that all the state constraints are not violated and the tracking error is preserved within a specified prescribed performance bound at all times, simultaneously. Then, by utilizing the mean value theorem, Nussbaum gain technique, a low-pass filter and a novel bounded estimation approach at each step of back-stepping procedure, a novel adaptive dynamics surface control scheme is developed to remove the difficulties of pure-feedback characteristic, unknown nonlinearities, unknown control direction and “explosion of complexity”, which can guarantee that the proposed design is universal and low-complexity. Moreover, it is proved that all the signals in the closed-loop system are global uniformly bounded. Two simulation studies are worked out to illustrate the performance of the proposed approach.

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Acknowledgements

This research was supported by the Aeronautical Science Foundation of China (2015ZC56007) and the Educational Commission of Jiangxi Province of China (GJJ150707, GJJ170610)

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  1. School of Aircraft Engineering, Nanchang Hangkong University, Nanchang, 330063, China

    Longsheng Chen & Qi Wang

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  1. Longsheng Chen
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Correspondence to Longsheng Chen.

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Chen, L., Wang, Q. Prescribed performance-barrier Lyapunov function for the adaptive control of unknown pure-feedback systems with full-state constraints. Nonlinear Dyn 95, 2443–2459 (2019). https://doi.org/10.1007/s11071-018-4704-1

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