# American Institute of Mathematical Sciences

doi: 10.3934/mcrf.2022024
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## Barrier Lyapunov functions-based adaptive neural tracking control for non-strict feedback stochastic nonlinear systems with full-state constraints: A command filter approach

 Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad (FUM), Mashhad, Iran

*Corresponding author: Seyed Kamal Hosseini Sani

Received  January 2022 Revised  April 2022 Early access May 2022

In this paper, an adaptive neural network command filter controller is investigated for a class of non-strict feedback stochastic nonlinear systems with full-state constraints. By using the command filter approach and error compensation mechanism, the "explosion of complexity" problem caused by the backstepping method and the filtering errors are eliminated. In order to avoid excessive and burdensome computations and to ensure that the backstepping method works normally for non-strict feedback structures, neural networks are employed to approximate the unknown nonlinear functions that contain all the state variables of the system. Meanwhile, the barrier Lyapunov functions are constructed to ensure the constraints are not transgressed. Finally, based on the Lyapunov stability theorem, an adaptive neural tracking controller is presented to guarantee that all the signals of the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) in probability, and the tracking error converges to a small neighborhood around the origin, besides the full-state constraints are not violated. The simulation results are given to confirm the effectiveness of the proposed control method.

Citation: Parisa Seifi, Seyed Kamal Hosseini Sani. Barrier Lyapunov functions-based adaptive neural tracking control for non-strict feedback stochastic nonlinear systems with full-state constraints: A command filter approach. Mathematical Control and Related Fields, doi: 10.3934/mcrf.2022024
##### References:

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##### References:
System output $y(t)$ and the reference signal $y_d(t)$
Tracking error $z_1$
Phase portrait of $z_1$ and $z_2$
System state $x_2$
Control signal $u$
Adaptive laws $\hat{\theta}_1$ and $\hat{\theta}_2$
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