The chaotic mobile robot

Adaptive Design of Controller and Synchronizer for Lu-Xiao Chaotic System with Unknown Parameters

“…V e e e e e e e e e e e e e e e e   = + + + + + + + (21) which is a positive definite function on 8 . R …”

“…which is a positive definite function on 8 . R A simple calculation from the equations (6) yields By differentiating the Lyapunov function V along the trajectories of (7) and using (9), we get…”

“…Chaos theory finds applications in many areas in science and engineering such as physical systems [2], chemical systems [3], ecology [4], biology [5], secure communications [6][7], robotics [8], etc.…”

Chaos Control and Synchronization of a Hyperchaotic Zhou System by Integral Sliding Mode control

“…In their seminal paper in 1990, Pecora and Carroll [10] introduced a method to synchronize two identical chaotic systems and showed that it was possible for some chaotic systems to be completely synchronized. Subsequently, chaos synchronization has been applied in a wide variety of fields, including physics [11], chemistry [12], ecology [13], secure communications [14,15], cardiology [16], robotics [17], complex dynamical networks [18], etc. Some common methods applied to the chaos synchronization problem are the active control method [19,20], adaptive control method [21,22], sampled-data feedback method [23], time-delay feedback method [24], backstepping method [25,26], sliding mode control method [27][28][29][30][31][32][33][34][35][36], etc.…”

Sliding Controller Design for the Global Chaos Synchronization of Identical Hyperchaotic Yujun Systems

“…Chaos synchronization has been applied in a wide variety of fields including physics [6], chemistry [7], ecology [8], secure communications [9][10], cardiology [11], neurology [12], robotics [13], etc.…”