Exponential stabilization of chaotic systems with delay by periodically intermittent control

Abstract

This paper studies the exponential stabilization problem for a class of chaotic systems with delay by means of periodically intermittent control. A unified exponential stability criterion, together with its simplified versions, is established by using Lyapunov function and differential inequality techniques. A suboptimal intermittent controller is designed with respect to the general cost function under the assumption that the control period is fixed. Numerical simulations on two chaotic oscillators are presented to verify the theoretical results.

Stabilization of Delayed Chaotic Neural Networks by Periodically Intermittent Control

“…In [10], the control period σ is assumed to be fixed and known, namely, σ = 0.5. However, Theorem 1 is free of this restriction.…”

“…This is called the periodically intermittent controller with three control parameters K, T and σ . In a recent work [10], such a control scheme was applied to exponential stabilization of a class of chaotic time-delay systems, where, however, the control duration is fixed as half of the control period, i.e., σ = 0.5. In this paper, we will remove this limitation and design a general periodically intermittent controller for chaotic time-delay neural networks.…”

Second-Order Consensus of Multi-agent Systems via Periodically Intermittent Pinning Control

“…As claimed and demonstrated in [1][2][3][4][5]8,9,13,18,26,29,30], consensus aimed at guiding the states of all agents to achieve a common value is one of the fundamental problems in the coordinated control of multi-agent systems and has attracted considerable attention, ranging from first-order systems [7,23] to second-order systems [10,12,14,20,31] and even high-order ones [21]. For example, the authors in [23] investigated the consensus of first-order multiagent systems subject to input saturation, whereas references [12,20,31] focused on the consensus of second-order multi-agent systems with nonlinear intrinsic dynamics.…”

Intermittent control of coexisting attractors

“…Also, previously proposed intermittent control laws [22,29] used the periodically time-driven control, whereas our method is event-driven control. where λ is a positive scalar.…”

“…In the control system literature, the term 'intermittent control' introduced by Ronco et al [21] has been adopted by a number of control methods [22,23] for different control purposes. It is worth noting that the concept of 'act-and-wait' control was proposed in Insperger [24], which was a form of intermittent control applied periodically [25].…”