A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems

Finite-time generalized synchronization of chaotic systems with different order

“…The error state trajectories converge to the origin in finite time. That is to say, the generalized synchronization is achieved between the chaotic systems (15) and (16) under the controller (19) in finite time. According to the simulation results, we can see the convergent time of the error system in Fig.…”

“…So, the study of synchronization for different order chaotic systems is very important to the perspective of control theory and practical application. Some theoretical results for the synchronization between different order chaotic systems have been obtained [12][13][14][15][16][17]. The synchronization is only attained by reduced order, because the order of the response system is lower than that of the drive system in [12][13][14][15].…”

Adaptive Control for the Stabilization and Synchronization of Nonlinear Gyroscopes

“…In our previous paper [51], we obtained a novel adaptive controller for chaos synchronization with unknown parameters. This is introduced in brief herein.…”

“…In [45] a novel adaptive controller for achieving chaos and hyperchaos synchronization was proposed. This adaptive control method was used to realize the synchronization of coupled RCL-shunted Josephson junctions [50] the reduced-order synchronization of time-varying systems [51] and extended to realize the stabilization of the unified chaotic system [52].This adaptive control method has better advantages than the linear feedback method, since the feedback gain k 1 is automatically adapted to a suitable gain k 0 depending on the initial values. It is not only simple in comparison with other previous methods, but also suitable for all chaotic systems and hyperchaotic systems.…”

Horizons of cybernetical physics

“…linear control [72,73], sample-data control [73], simple adaptive control [74], sliding mode control [75,76], etc. A lot of attention was devoted to controlled synchronization of fractional-order systems [75,77,78].…”