Doctorat LMD
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Item Advanced Analysis and Robust Control for Chaotic Systems Analyse Avancée et Commande Robuste des Systèmes Chaotiques(Faculté des sciences et de la technologie, 2025-04-10) Salah Eddine SAADIChaos control, chaos analysis, and chaotification in dynamical systems have received increasing attention from research communities and have been extensively studied. Recently, chaotic synchronization and chaotic sys-tems with higher-dimensional attractors, known as hyperchaotic systems, have found a wide range of applications, receiving sustained and fervent attention across several fields. This work focuses primarily on the control, model-ing, and synchronization of chaotic systems, using a new family of nonlinear control algorithms based on Lya-punov synthesis, terminal attractor theory, and fuzzy modeling, combined with recent amalgamations of robust control techniques, namely terminal sliding mode control and terminal synergetic control. First, an adaptive ter-minal sliding mode control law was developed and validated through simulations for controlling certain hyper-chaotic systems. Then, fuzzy modeling and its combination with synergetic control were developed to provide a new algorithm for the synchronization of two different hyperchaotic systems. The final part of this work is devoted to the synchronization of chaotic systems using a new concept of terminal synergetic adaptive control. This ap-proach aims to circumvent the drawback of asymptotic convergence in the design of the synergetic control law and to overcome various issues related to chaotic systems, including mathematical model accuracy, parametric uncertainties, and external disturbances, thus enabling easy real-time implementation of the control law. Simula-tion tests were conducted to assess the effectiveness of the proposed algorithms.