Adaptive dynamic surface asymptotic tracking control of uncertain strict‐feedback systems with guaranteed transient performance and accurate parameter estimation

• Published in: International journal of robust and nonlinear control Vol. 32; no. 12; pp. 6829 - 6848
• Main Authors: Shi, Wenrui, Hou, Mingzhe, Duan, Guangren, Hao, Mingrui
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.08.2022
• Subjects: Adaptive control; Algorithms; Asymptotic properties; asymptotic tracking; Control algorithms; Control theory; D C motors; dynamic surface control; Electric motors; Feedback; Forecasting; Operators (mathematics); Parameter estimation; projection operator; Robust control; Tracking control; Tracking errors; Transient performance
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6170

In this article, an adaptive dynamic surface control approach is proposed for uncertain strict‐feedback systems (SFSs) to guarantee both the prescribed transient tracking performance and the asymptotic tracking while realizing the accurate parameter estimation. It is assumed that SFSs are subject to linearly parametric uncertainties in both the drift terms and the control coefficients. A new inequality on the arctangent function, which can be widely used in the robust or the adaptive control designs, is established. Owing to this inequality, nonlinear robust filters with arctangent functions are designed and embedded into the backstepping control algorithm to avoid the “differential explosion” problem. Moreover, an improved forgetting‐factor‐based parameter estimation error reconstruction mechanism is proposed. And the obtained parameter estimation errors are integrated into the adaptive laws to achieve the accurate parameter estimation. Furthermore, the projection operator is applied to avoid the singularity problem of the control law. Besides, an asymmetric error transformation is introduced to restrict the tracking error within the prescribed performance envelope. It is proved that the tracking error and the parameter estimation errors asymptotically converge to zero and the tracking error satisfies the prescribed transient performance. Finally, the effectiveness of the proposed control approach is validated in terms of the single‐link manipulator actuated by a brush DC motor.