Command filtered adaptive neural network synchronization control of fractional-order chaotic systems subject to unknown dead zones

• Published in: Journal of the Franklin Institute Vol. 358; no. 7; pp. 3376 - 3402
• Main Authors: Ha, Shumin, Chen, Liangyun, Liu, Heng
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.05.2021; Elsevier Science Ltd
• Subjects: Adaptive control; Chaos theory; Control methods; Error compensation; Fractions; Liapunov functions; Mathematical functions; Neural networks; Nonlinear equations; Radial basis function; Stability; Subsystems; Synchronism; Systems stability
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.02.012

Command filters are essential for alleviating the inherent computational complexity (ICC) of the standard backstepping control method. This paper addresses the synchronization control scheme for an uncertain fractional-order chaotic system (FOCS) subject to unknown dead zone input (DZI) based on a fractional-order command filter (FCF). A virtual control function (VCF) and its fractional-order derivative are approximated by the output of the FCF. In order to handle filtering errors and obtain good control performance, an error compensation mechanism (ECM) is developed. A radial basis function neural network (RBFNN) is introduced to relax the requirement of the uncertain function must be linear in the standard backstepping control method. The construction of a VCF in each step satisfies the Lyapunov function to ensure the stability of the corresponding subsystem. By using the bounded information to cope with the unknown DZI, the stability of the synchronization error system is guaranteed. Finally, simulation results verify the effectiveness of our methods.