Implementation of T-S fuzzy approach for the synchronization and stabilization of non-integer-order complex systems with input saturation at a guaranteed cost

Abstract

One of the fundamental topics in engineering that has many applications in applied sciences is guaranteed cost control and synchronization of chaotic dynamical systems. In this paper, a Takagi–Sugeno (T-S) fuzzy model-free state feedback (MFSF) technique is used to synchronize and stabilize various complex fractional-order systems (FOSs) in the presence of input saturation. A T-S fuzzy MFSF method is developed to suppress the inappropriate behavior of the FOSs without any unpleasant chattering phenomena using the non-integer form of the Lyapunov stability theory (LST) and linear matrix inequality concept. The suggested MFSF technique may be used to stabilize and synchronize FOSs with model uncertainty, external disturbances, and input saturation. The designed method has the advantages of being a model-free technique, being resistant to uncertainties, being simple to use, and achieving the equilibrium point quickly at a guaranteed cost. Furthermore, the effectiveness and application of the T-S fuzzy MFSF are proven using the suggested approach to synchronize two separate canonical chaotic FOSs and stabilize the permanent magnet synchronous motor (PMSM) chaotic system. Two comparisons demonstrate the efficacy and advantages of the T-S fuzzy approach over other existing control methods.

A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

“…Theorem 5. Suppose the FO laser chaotic mechanism (12). Then, by operating the following control methodology (35), the process of trajectories of the FO laser chaotic mechanism (12) will exhibit asymptotic stability in finite-time.…”

“…V 3 < 0. Hence, the stabilization criteria in Theory 2 are derived, and trajectories of the FO laser chaotic mechanism (12) will convergence to the origin. Now, based on ( 28) and (46), we have .…”

“…Consequently, the research community has directed its efforts towards devising diverse methodologies for the control and synchronization of chaotic FO systems. Within this context, a plethora of control strategies have been proposed, encompassing techniques such as the SMC controller [11], fuzzy controller [12,13], PID controller [14], observer controller [15], adaptive controller [16], and optimal controller [17], all aimed at governing and harmonizing the dynamics of chaotic FO systems.…”

Power-exponential and fixed-time consensus of conformable fractional-order quantum cellular neural networks via event-triggered control

“…As an important dynamic behavior of chaotic systems, synchronization exists widely in application areas such as cryptographic construction systems, fault diagnosis systems, multiuser detection systems, and image watermarking systems [28][29][30][31][32][33][34][35][36][37]. During the past several years, various kinds of synchronization have been proposed in control science, such as asymptotic synchronization and finite-time synchronization.…”

Finite-time sliding mode control methods for a class of non-integer-order systems with input saturations and its application

“…As a direct consequence of this, the primary emphasis of the research community has been the development of a variety of strategies for the control and synchronization of chaotic FO systems. In this context, a number of different control methodologies have been proposed, including the sliding mode controller [9,10], the adaptive controller [11,12], the fuzzy controller [13], the feedback controller [14], the PID controller [15], the observer controller [16], and the optimal controller [17,18] to control and synchronize of chaotic FO systems.…”