Model-free adaptive backstepping control for a class of uncertain nonlinear systems

• Published in: Transactions of the Institute of Measurement and Control 2024-04, Vol.46 (7), p.1317-1330
• Main Authors: Segheri, Mohamed, Boudjemaa, Fares, Nemra, Abdelkrim, Bibi, Youssouf
• Format: Article
• Language: English
• Subjects: Adaptive control; Dynamical systems; Liapunov functions; Mathematical models; Nonlinear dynamics; Nonlinear systems; Parameters; Petri nets; Uncertainty
• ISSN: 0142-3312; 1477-0369
• DOI: 10.1177/01423312231189380

Most nonlinear dynamic systems are characterized by uncertainties in models and parameters. Deterministic models cannot account for these uncertainties; therefore, model-based control using such models cannot provide the required performance. It is crucial to establish a practical concept of model-free control as a powerful alternative to model-based control. This paper develops a model-free adaptive backstepping control (MFABC) based on type 2 fuzzy Petri nets for a class of uncertain nonlinear systems. To provide valuable robustness to the MFABC structure, we have exploited the universal approximation property of type 2 fuzzy Petri nets to approximate the different nonlinear functions of the uncertain nonlinear system. The parameter adaptive laws are designed by the Lyapunov function; the stability and error convergence can be guaranteed. The simulation tests show that the proposed MFABC can provide good performance and high accuracy compared with the backstepping control. Moreover, the stability of this control scheme is affirmed.