TY - JOUR
T1 - Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying Pseudo-state constraints
AU - ZOUARI, Farouk
AU - IBEAS, Asier
AU - BOULKROUNE, Abdesselem
AU - CAO, Jinde
AU - AREFI, Mohammad Mehdi
N1 - Publisher Copyright:
© 2021 Elsevier Ltd
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/3
Y1 - 2021/3
N2 - This article considers the neural adaptive control issues of a category of non-integer-order non-square plants with actuator Nonlinearities and Asymmetric Time-Varying pseudo-State Constraints. First, the original non-square non-affine system with input nonlinearities is transformed into an equivalent affine-in-control square model by defining a set of auxiliary variables and by employing the mean-value theorem. Second, Neural networks and Nussbaum functions are exploited to obviate the requirement of a complete knowledge of the system dynamics and the control directions, respectively. Third, a novel adaptive dynamic surface control method based on Caputo fractional derivative definitions and fractional order filters is developed to overcome the “explosion of complexity” problem in the traditional backstepping design process and to determine the parameter update laws and control signals, concurrently. Then, Asymmetric Barrier Lyapunov Functions with error variables are adopted to ensure the uniform stability of the closed-loop system and to prevent the violation of the full pseudo-State constraints. The novelties and contributions of this article are: (1) through the introduction of new technical Lemmas and corollaries, existing control design and stability theories linked to integer-order square systems are developed and extended to non-square non-integer-order ones. (2) all signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints. Finally, the effectiveness and potential of the proposed control approach are substantiated by two example simulations.
AB - This article considers the neural adaptive control issues of a category of non-integer-order non-square plants with actuator Nonlinearities and Asymmetric Time-Varying pseudo-State Constraints. First, the original non-square non-affine system with input nonlinearities is transformed into an equivalent affine-in-control square model by defining a set of auxiliary variables and by employing the mean-value theorem. Second, Neural networks and Nussbaum functions are exploited to obviate the requirement of a complete knowledge of the system dynamics and the control directions, respectively. Third, a novel adaptive dynamic surface control method based on Caputo fractional derivative definitions and fractional order filters is developed to overcome the “explosion of complexity” problem in the traditional backstepping design process and to determine the parameter update laws and control signals, concurrently. Then, Asymmetric Barrier Lyapunov Functions with error variables are adopted to ensure the uniform stability of the closed-loop system and to prevent the violation of the full pseudo-State constraints. The novelties and contributions of this article are: (1) through the introduction of new technical Lemmas and corollaries, existing control design and stability theories linked to integer-order square systems are developed and extended to non-square non-integer-order ones. (2) all signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints. Finally, the effectiveness and potential of the proposed control approach are substantiated by two example simulations.
KW - Adaptive control
KW - Asymmetric Barrier Lyapunov functions
KW - Backstepping design process
KW - dynamic surface control method
KW - Neural Networks
KW - Non-integer-order non-square plants
KW - Nussbaum functions
UR - http://www.scopus.com/inward/record.url?scp=85100478259&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2021.110742
DO - 10.1016/j.chaos.2021.110742
M3 - Article
AN - SCOPUS:85100478259
VL - 144
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
SN - 0960-0779
M1 - 110742
ER -