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Direct Adaptive Fuzzy Tracking Control of Non-affine Stochastic Nonlinear Time-Delay Systems

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Abstract

In this research, the problem of direct adaptive fuzzy control based on state feedback for a class of non-affine stochastic nonlinear systems with time delay is considered. Fuzzy logic systems (FLSs) and mean value theorem are utilized to overcome the design difficulties appeared in the unknown nonlinearities and non-affine structure, respectively. With the utilization of adaptive control and backstepping design framework, a direct adaptive fuzzy control method is developed. Through Lyapunov analysis, the presented controller can guarantee that the variables in the closed-loop system are all bounded in the fourth-moment, in the mean time, the output signal can track the given reference signal by appropriately selecting the design parameters. Simulation results are provided to illustrate the correctness of the theoretical results.

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Acknowledgements

This work is supported in part by the National Natural Science Foundation of China (under Grant Nos. 61773072, 51939001, 61976033), and in part by the Natural Science Foundation of Liaoning Province of China under Grant 20180550691 and 20180550590 and the Taishan Scholar Project of Shandong Province of China under Grant 2015162 and tsqn201812093.

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Wang, H., Shan, L., Zhao, X. et al. Direct Adaptive Fuzzy Tracking Control of Non-affine Stochastic Nonlinear Time-Delay Systems. Int. J. Fuzzy Syst. 23, 309–321 (2021). https://doi.org/10.1007/s40815-020-00925-7

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