Exponential Synchronization for Delayed Dynamical Networks via Intermittent Control: Dealing With Actuator Saturations
Exponential Synchronization for Delayed Dynamical Networks via Intermittent Control: Dealing With Actuator Saturations
复制标题
通过间歇控制实现延迟动态网络的指数同步：处理执行器饱和
DOI：
10.1109/tnnls.2018.2854841
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发表时间：
2019-04
影响因子：
10.4
通讯作者：
董宏丽
中科院分区：
文献类型：
--
作者：
陈永刚;王子栋;沈波;董宏丽
在过去的二十年里，动态网络的同步问题由于其在生物系统、社交网络和神经科学中的清晰的实践洞察力而引起了极大的关注。当动态网络本身无法实现同步时，应添加反馈控制器来驱动网络走向期望的轨道。另一方面，时滞往往发生在动态网络的节点或耦合处，时滞的存在可能会导致一些不期望的动态甚至不稳定。此外，在实施反馈控制器的过程中，不可避免的执行器限制可能会降低系统性能，并且在最坏的情况下，会使闭环动态不稳定。研究了一类具有执行器饱和的时滞动态网络的同步问题。将动态网络的每个节点用一个具有时变时滞的非线性系统来描述，并提出了间歇控制策略。通过结合新的扇区条件、分段Lyapunov泛函和切换系统方法，首先得到了动态网络局部指数同步的时滞相关充分条件.然后，通过矩阵不等式的可行性建立了控制器增益的显式表征。此外，优化问题，制定，以获得一个更大的估计的初始条件的一组演变的误差动态时，设计间歇控制器。最后，通过两个算例说明了理论结果的有效性。
Over the past two decades, the synchronization problem for dynamical networks has drawn significant attention due to its clear practical insight in biological systems, social networks, and neuroscience. In the case where a dynamical network cannot achieve the synchronization by itself, the feedback controller should be added to drive the network toward a desired orbit. On the other hand, the time delays may often occur in the nodes or the couplings of a dynamical network, and the existence of time delays may induce some undesirable dynamics or even instability. Moreover, in the course of implementing a feedback controller, the inevitable actuator limitations could downgrade the system performance and, in the worst case, destabilize the closed-loop dynamics. The main purpose of this paper is to consider the synchronization problem for a class of delayed dynamical networks with actuator saturations. Each node of the dynamical network is described by a nonlinear system with a time-varying delay and the intermittent control strategy is proposed. By using a combination of novel sector conditions, piecewise Lyapunov-like functionals and the switched system approach, delay-dependent sufficient conditions are first obtained under which the dynamical network is locally exponentially synchronized. Then, the explicit characterization of the controller gains is established by means of the feasibility of certain matrix inequalities. Furthermore, optimization problems are formulated in order to acquire a larger estimate of the set of initial conditions for the evolution of the error dynamics when designing the intermittent controller. Finally, two examples are given to show the benefits and effectiveness of the developed theoretical results.
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