Sliding mode control for a class of chaotic systems

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

“…The response of the slave hyperchaotic Zhou system in Equation (26) with the arbitrary initial condition y(0) ∈ R 4 , using the control laws in Equation (32) with λ i , η i , k i > 0 and the adaption laws in Equation (33), tends toward the response of the master system in Equation (25) with unknown parameters. This means that the error signals in Equation (27) and the parameter errors in Equation (29) are globally asymptotically stable and converge to zero.…”

“…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. In this paper, a new scheme based on the adaptive integral sliding mode control for the chaos synchronization of two identical hyperchaotic Zhou systems [37] is derived.…”

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

“…A seminal paper on chaotic synchronization was published by Pecora and Carroll [14], which paved the way for several new methods such as the active control method [15][16], adaptive control method [17][18][19][20], sampled-data feedback method [21], time-delay feedback method [22], backstepping method [23][24], sliding mode control method [25][26], etc. This paper derives new results for the sliding controller design for the global chaos synchronization of identical hyperchaotic Yujun systems ([29], 2010).…”

Adaptive Control and Synchronization of the Cai System

“…The pioneering work by Pecora and Carroll (1990) has been followed by a variety of impressive approaches in the literature such as the sampled-data feedback method [11], OGY method [12], time-delay feedback method [13], backstepping method [14], active control method [15][16][17][18][19][20], adaptive control method [21][22][23][24][25], sliding mode control method [26][27][28], etc. This paper is organized as follows.…”