43 Delayed Feedbac Control Delayed Feedbac Control Prediction-based Feedbac Control 1, 2 GDP
44 66 3 3 2 Ott, Grebogi Yore OGY 4 OGY OGY OGY OGY OGY 3, 5, 6 OGY Pyragas Delayed Feedbac Control DFC 7 DFC 2 DFC OGY 3, 8, 9, 1 DFC DFC 11, 12
45 2 Delayed Feedbac Control Delayed Feedbac Control 3 Delayed Feedbac Control Prediction-based Feedbac 4 5 Delayed Feedbac Control DFC 7 f R n R n n x 1 f x K x τ x, 1 K R n n Z τ Z x R n 1 K x τ x Delayed Feedbac Control K τ K τ DFC x τ x x τ x τ DFC DFC
46 66 3 x 1 ax 1 x, 2 a a 3.5699 a 3.7 x 1 ax 1 x K x τ x. 3 K 2 2 x f 1, x f 2 x f 1 a 1 a, x f 2. 2 2 δx i 1 a 2ax fi δx i, 4 δx x i x fi, i 1, 2 2 x fi, i 1, 2 1 τ 1 K x 1 x x 1 ax 1 x K x 1 x, 5 w x 1 x 1 ax 1 x K w x, 6 w 1 x. 7 1 2
47 6 7 x fi, i 1, 2 δx i 1 a 2ax fi K K δx i δw i 1 1 δw i 8 δx x i x fi, δw w i x fi, i 1, 2 x f 1 DFC x f 1 2 4 a 2ax f 1 2 a a 3.7 2 a 1 x f 1 x f 1 DFC 5 x f 1 8 1 1 K 3 a 2 K x f 1 Jury 13 x f 2 DFC x f 2 x f 2 DFC 11, 12 1 DFC x f 2 x f 2 4 a a 3.7 x f 2 1
48 66 3 x f 2 DFC 6 7 x f 2 a K K 1 a 3.7 2 1 1 Jury K x f 2 DFC 1 Prediction-based Feedbac Control PFC 14, 15, 16 DFC τ PFC τ u K x τ x, x R n K x τ τ PFC x 1 f x K x 1 x 9 DFC PFC DFC PFC
49 PFC 17 PFC 1 x f 1, x f 2 PFC x 1 ax 1 x K x 1 x, 1 a 2 x fi, i 1, 2 δx i 1 2a 1 K x fi a ak K δx i, 11 δx i x x fi. DFC 1 K 2 2a 1 K x fi a ak K 1. 12 DFC x f 2 PFC x f 2 12 a 1 1 a K 1 K PFC DFC PFC x τ 1
5 66 3 u K x p τ x, x p τ τ PFC x τ x p τ PFC 18, 19 2 PFC 1 16 u x 1 f x, u. 13 τ u K x p τ x, K x p τ 13 x 1 f x, τ PFC PFC u K x τ x
51 DFC 7 u K x τ x PFC 14, 15 PFC 2 x system x system f x system, x data x data x data f x data, x system τ x p τ x data f x data, t p x data t p x data x system 1 x data, t p x system f x system, x system τ x system 13 x x data τ x system τ x * τ x p τ x * τ u K x p τ x K x * τ x x 1 3.7x 1 x x data, x system τ x system 1 τ data t p 1 x data x system x p x system t p τ * data τ 1 1 data
52 66 3 x p x τ system t p x data x system t p τ t p data x system x τ 1 1.31.21.1 1.31.21.6 5.31.21.45 1.31.21.241 τ 5 1.41.11.6 1.41.11.81 5.41.11.142 1.41.11.957 τ 1 1.41.11.7 1.41.11.187 1.41.11.663 radial basis function 19 PFC a 3.7 x 1 3.7x 1 x. 14 x 1 PFC 14 x 1 3.7x 1 x K x p τ x,
53 x 1.8.6.4.2 2 4 6 8 1 2 15 1 5.1.2.3.4.5.6.7.8.9 1 x x distribution function of x, P(x) x p τ 14 τ K u K x p τ x, if x τ x.1,, otherwise. 15 x fp a 1 a.7297 12 K.5 12 K x τ x K x p τ x 12 K x p τ 12 K 2 x p t p 1 2 x x fp.7297
54 66 3 x 1.8.6.4.2 2 4 6 8 1 distribution function of x, P(x) 5 4 3 2 1.2.4.6.8 1 x K.5 t p 1 x x 1.8.6.4.2 1 2 3 4 5 distribution function of x, P(x) 5 4 3 2 1.2.4.6.8 1 x K.5 t p 5 x 3 t p 5 3 x x fp.7297 1 t p 5 4 t p 1
55 x 1.8.6.4.2 2 4 6 8 1 K.5 t p 1 x distribution function of x, P(x) 2 15 1 5.2.4.6.8 1 x t p.1 t p 1 1 5 1 1 1 5 6 2 3 1 4 x fp 2 t p.1 1 1 2 t p 1
56 66 3 8 Delayed Feedbac Control DFC Prediction-based Feedbac Control PFC DFC PFC 21, 22 DFC 23 Delayed Feedbac Control DFC PFC PFC DFC x 1 f x, x τ1, x τ2 x τ2
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