By Housheng Su, Xiaofan Wang
Synchronization, consensus and flocking are ubiquitous standards in networked platforms. Pinning keep watch over of advanced Networked structures investigates those requisites by utilizing the pinning regulate method, which goals to regulate the full dynamical community with large numbers of nodes by means of enforcing controllers for just a fraction of the nodes. because the direct regulate of each node in a dynamical community with large numbers of nodes could be most unlikely or pointless, it’s then vitally important to exploit the pinning regulate procedure for the synchronization of complicated dynamical networks. The examine on pinning keep watch over technique in consensus and flocking of multi-agent platforms cannot purely support us to raised comprehend the mechanisms of usual collective phenomena, but in addition profit functions in cellular sensor/robot networks. This e-book bargains a priceless source for researchers and engineers operating within the fields of keep watch over idea and regulate engineering. Housheng Su is an affiliate Professor on the division of keep watch over technology and Engineering, Huazhong collage of technological know-how and know-how, China; Xiaofan Wang is a Professor on the division of Automation, Shanghai Jiao Tong collage, China.
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Extra resources for Pinning Control of Complex Networked Systems: Synchronization, Consensus and Flocking of Networked Systems via Pinning
Example text
This controlled network can be described as N x˙ik = f (xik ) + cik j aik j Γ (xj − xik ) + uik , k = 1, 2, . . 3) cik j aik j Γ (xj − xik ), k = l + 1, l + 2, . . , N. j =1,j =ik For simplicity, we use the local linear negative feedback control law as follows: uik = −cik ik dik Γ (xik − x), ¯ k = 1, 2, . . 4) where the coupling strength cik ik satisfies cik ik aik ik + N j =1,j =ik cik j aik j = 0, and the feedback gain dik > 0. Without loss of generality, we rearrange the order of nodes in the network such that the pinned nodes ik , k = 1, 2, .
3). Then N N (xi − x iˆ )T P ˆ jˆ,j =i j =1,i= i=1 = aij cij (xi − xj ) 1 2 N N hij aij cij (xi − xj )T P (xi − xj ). 5) i=1 j =1,i= ˆ jˆ,j =i where x˜i = xi − x iˆ . 2 Decentralized Adaptive Pinning Control Scheme 49 N N = aij cij x˜iT P (x˜i − x˜j ). 7). 7), N N (xi − x iˆ )T P = aij cij (xi − xj ) ˆ jˆ,j =i j =1,i= i=1 1 2 N N hij aij cij (xi − xj )T P (xi − xj ). 5 [6] If a scalar function V (x, t) satisfies the following conditions: (a) (b) (c) V (x, t) is lower bounded; V˙ (x, t) is negative semi-definite; V˙ (x, t) is uniformly continuous in t; then V˙ (x, t) → 0, as t → ∞.
This phenomenon will be visually illustrated in the simulation study below. Pinning strategies mainly include random pinning and specific pinning schemes. In the random pinning scheme, we apply local feedback injections to a fraction δ of randomly selected nodes. While in the specific pinning scheme, we first pin the node of the highest degree, and then continue to select and pin the other nodes in a monotonically decreasing order of degrees. In a star-like structure of a dynamical network, the kernel node is specifically selected to control for stabilizing the whole network.
