By Hongwei Wang, Hong Gu (auth.), Derong Liu, Shumin Fei, Zengguang Hou, Huaguang Zhang, Changyin Sun (eds.)

This booklet is a part of a 3 quantity set that constitutes the refereed complaints of the 4th foreign Symposium on Neural Networks, ISNN 2007, held in Nanjing, China in June 2007.

The 262 revised lengthy papers and 192 revised brief papers offered have been rigorously reviewed and chosen from a complete of 1,975 submissions. The papers are geared up in topical sections on neural fuzzy keep an eye on, neural networks for regulate functions, adaptive dynamic programming and reinforcement studying, neural networks for nonlinear platforms modeling, robotics, balance research of neural networks, studying and approximation, information mining and have extraction, chaos and synchronization, neural fuzzy platforms, education and studying algorithms for neural networks, neural community constructions, neural networks for development reputation, SOMs, ICA/PCA, biomedical functions, feedforward neural networks, recurrent neural networks, neural networks for optimization, help vector machines, fault diagnosis/detection, communications and sign processing, image/video processing, and purposes of neural networks.

**Read or Download Advances in Neural Networks – ISNN 2007: 4th International Symposium on Neural Networks, ISNN 2007, Nanjing, China, June 3-7, 2007, Proceedings, Part II PDF**

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**Extra info for Advances in Neural Networks – ISNN 2007: 4th International Symposium on Neural Networks, ISNN 2007, Nanjing, China, June 3-7, 2007, Proceedings, Part II**

**Example text**

Xiang, J. Zhou, and Z. Liu implies that zero is an eigenvalue of B with multiplicity 1 and all the other eigenvalues of B are strictly negative [3]. Next, we consider the issues of impulsive control for robust synchronization of the coupled delayed neural network (1). By adding an impulsive controller {tk , Iik (t, xi (t))} to the ith-dynamical node in the coupled delayed neural network (1), we have the following impulsively controlled coupled delayed neural network: ⎧ x˙ i (t) = −Cxi (t) + Af (xi (t)) + Aτ g(xi (t − τ )) + I(t) ⎪ ⎪ ⎪ N ⎨ bij Γ xj (t), t = tk , t ≥ t0 , + (2) ⎪ ⎪ j=1 ⎪ ⎩ xi = Iik (t, xi (t)), t = tk , k = 1, 2, · · · , where i = 1, 2 · · · , N , the time sequence {tk }+∞ k=1 satisfy tk−1 < tk and limk→∞ tk = − +∞, xi = xi (t+ ) − x (t ) is the control law in which xi (t+ i k k k ) = limt→t+ xi (t) and k xi (t).

Li, and Y. Yang =e t N −1 N {(xi (t) − xj (t))T [( P1 − 2P1 C)(xi (t) − xj (t)) i=1 j=i+1 +2(P1 A − N Gij P1 D)(f (xi (t)) − f (xj (t))) +2P1 B(f (xi (t − τ )) − f (xj (t − τ )))] +e τ (f (xi (t)) − f (xj (t)))T P2 (f (xi (t)) − f (xj (t))) −(f (xi (t − τ )) − f (xj (t − τ )))T P2 (f (xi (t − τ )) − f (xj (t − τ ))) +e τ (xi (t) − xj (t))T P3 (xi (t) − xj (t)) −(xi (t − τ ) − xj (t − τ ))T P3 (xi (t − τ ) − xj (t − τ ))}; (8) Under the assumption (H), one can easily get the following inequalities (f (xi (t)) − f (xj (t)))T S(f (xi (t)) − f (xj (t))) ≤ (xi (t) − xj (t))T LS(f (xi (t)) − f (xj (t))), (f (xi (t − τ )) − f (xj (t − τ )))T W (f (xi (t − τ )) − f (xj (t − τ ))) ≤ (xi (t − τ ) − xj (t − τ ))T LW (f (xi (t − τ )) − f (xj (t − τ ))), (9) (10) where 1 ≤ i < j ≤ N .

Guan, and T. Li 3 Synchronization Between Unified Chaotic System and Genesio System Via Active Control In order to observe the synchronization behavior between unified chaotic system and Genesio system via active control, we assume that Genesio system (2) is the drive system and the controlled unified chaotic system (4) is the response system. ⎧ x1 = (25α + 10)( y1 − x1 ) + u1 ⎪ ⎨ y1 = (28 − 35α ) x1 + (29α − 1) y1 − x1 z1 + u2 ⎪⎩ z1 = x1 y1 − 8 +3α z1 + u3 (4) Three control functions u1 , u2 , u3 are introduced in system (4), in order to determine the control functions to realize synchronization between systems (2) and (4), we subtract (2) from (4) and get ⎧ e1 = (25 + α )( y1 − x1 ) − y + u1 ⎪ ⎨ e2 = (28 − 35α ) x1 + (29α − 1) y1 − x1 z1 − z + u2 ⎪⎩ e3 = x1 y1 − 8 +α z1 − ax − by − cz − x 2 + u3 3 (5) where e1 = x1 − x, e2 = y1 − y, e3 = z1 − z , we define active control functions u1 , u2 and u3 as follows ⎧ u1 = −(25α + 10)( y1 − x) + y + V1 ⎪ ⎨ u2 = −(28 − 35α ) x1 − (29α − 1) y + x1 z1 + z + V2 ⎪⎩ u3 = − x1 y1 + 8 +α z + ax + by + cz + x 2 + V3 3 (6) Hence the error system (5) becomes ⎧ e1 = −(25α + 10)e1 + V1 ⎪ ⎨ e2 = (29α − 1)e2 + V2 ⎪⎩ e3 = − 8 +3α e3 + V3 (7) The error system (7) to be controlled is a linear system with control inputs V1 ,V2 and V3 as functions of the error states e1 , e2 and e3 .