強化学習と小脳モデルを利用した適応型制御システムの設計法

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(13) 1 (Feedback Error Learning FEL). (Auto-Fusion Cerebellar Perceptron Robust Control System AFCPRCS).

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(18) 2.2 2.2.1 x1. m. x2. ((2.1) ). n. u. ). x1. ( m). f 1 ( x1 , x 2 ). g1 (x1 , x 2 ) u. ( n). f 2 ( x1 , x 2 ). g 2 ( x1 , x 2 ) u. x2 x1. [ x1 , x1 , u. , x1. ( m 1) T. ]. Rm , x2. [ x2 , x x ,. , x2. ( n 1) T. ]. [ x1r , x1r , , x1r. Rn. f1 (x1 , x 2 ), f 2 (x1 , x 2 ), g1 (x1 , x 2 ), g 2 (x1 , x 2 ). R. x1 , x 2 x1r. ((2.2). x1 , x 2. ( m 1) T. ] , x 2r. [ x2 r ,. , x2r ,. ,x. ( n 1) T 2r. ]. (2.1)(2.2). 2.2.2. (1) (2) (3) (4). Actor-Critic.

(19) 2.2.3. Actor-Critic. Actor-Critic. (2.1). Actor-Critic. m. TD Temporal Difference Fig.3.1 Actor. ur. system. V. RBF (Radial Basis Function). ur ur. Actor-Critic. (2.3) J. 1 exp ur. w jb j x1. nt. j 1. U max. J. 1 exp. (2.3) w jb j x1. nt. j 1. wj. J. U max. j. b j x1. Critic. nt. TD. V. TD. 1). a. Critic. TD. (2.4). t a (0. j. rt. aV. t 1 Vt. rt. (2.4). TD. Actor. RBF. (2.5). V t. V t. J. w j b j x1. (2.5). j 1. Critic. Actor. RBF sigmoid (6). b j x1. (2.6). b j x1. exp. I i 1. xi. I. i Critic. TD. xi. c ji. 2. (2.6). 2 ji. x1. i. j. c ji. 2 ji. Actor.

(20) V t. nt. ur t. rt. x1 t. Fig.2.1.. Construction of Actor-Critic control system.. ua x2 t. e. x 2r Fig.2.2.. Construction of adaptive H control system..

(21) Actor RBF. Back Propagation(BP). Critic. wcri j. 1 V 2. V wcri j. cri w. 2. (2.7). Actor. wact j cri. act. Critic. 2.2.4. u wact j. act w. n. (2.8) cri w. Actor. ,. act w. H (2). Fig.2.2. H. H. x2. e. x 2r. e (adaptor) (2.10). x2. (2.9). x 2r. (2.9). controller. (2.2) f 2 x1, x2 , g2 x1, x2. n g 2 x1 , x 2. x2 x2. x2 , x2 , , x2 n. 1 T. ( n). f 2 (x 1 , x 2 ) xm 1, xm 2 , , xn. m. T. g 2 (x 1 , x 2 ) u a. (2.10). H. ua. (2.10). x2. Ax B f2 (x1, x2 ) g2 (x1, x2 )ua. (2.11).

(22) 0 0. 1 0. 0 1. 0. 0 0. A. 0 B. , 0. 0. 0. 1. 0. 0. 0. 0. 0. 1. (Riccati) P. A T P PA. PBB T P Q. 0. (2.12). ua. (adaptor). sl x 2. RBF. N. sl x 2. exp. xn. 2 m. ln. (2.13). 2 ln. n 1. H nn. (2.13). (2.14) L. sl2 x 2. H nn. (2.14). l 1. N ln. xn. L n. l. n m. m. 2 ln. (2.15). c. if c and otherwise,. 0,. c. (2.15) (2.16). c. 1. x 2 eT PBB T Pe 1. x2. 2. x2 1. 1 c. H nn. (2.19). 1 H nn 12. x 2 B T Pe. (2.16) (2.17) (2.18). (2.19) 1.

(23) (controller). ua. system. ua. x 2 BT Pe. ua. (2.20). x 2 sgn B T Pe. (2.20). sgn. 1 ( 1 (. sgn ( ). (2.21). H. 1. (2.20). 0) 0). 2 [19]. 2.2.5. H. Fig.3.3 (2.1)(2.2) (2.1) (2.2). Actor. x1. H. x2. 2 ua. system. u. (2.22). x1. ur. 2.2.3 ua. ur. 2.2.4 (2.1)(2.2). x2. 2. (2.1)(2.2). x1 , x2. x 2 (2.2). (2.1). x1. H. 2. 1 H. H. H. 1. 2 2.2.3.

(24) u (0. ua. 1. ur. (2.22). 1) x1. x2. V. n. ur r. x1. u. ua. x2. e. x 2r Fig.2.3. Proposed cooperated control system..

(25) 2.3 2.3.1 Fig.2.4. g sin l. ml cos m M. x. x. F g xt. m cos 2 m M. 1 sin 2 2. cos F m l. ml sin m M. 1 m M. xr. m. (2.23). F. (2.24) M. t. l. 0. t , t , xt , xt. Actor-Critic. M x, dx / dt , d 2 x / dt 2. F. xr. , d / dt d 2 / dt 2 mg. Fig.2.4.. Overhead traveling crane system..

(26) m 0.5 kg. M. 1.0 kg. l. 0.5 m. Table 2.1. 9.8 m s 2. g. 1. H. Actor-Critic. H. 2. ur. , ua 2. Parameters. I J N. L Q. Proposed method 1 2 35 2 25 0.5 diag {0.4,0.4}. 2 2 25 0.5 diag. Actor-Critic method (Conventional method) 4 49 -. {0.24,0.24} for u a. diag {0.01,0.01} for u r. c. 1. U max a r. r x r v r cri w act w. 0.002 0.1 0.5 1.0 0.01 3.0 0.95 1.0 1.0 4.0 20.0 0.05 0.05. 0.002 0.1 0.5 1.0 0.01 -. 3.0 0.95 0.2 20.0 4.0 20.0 0.02 0.02.

(27) 2.3.2 10. 0. 0.02. 40. 45. 10m. H. 1. 5 ±0.25[m] 1 1. x1r. Actor-Critic T. x1r , x1r. x r ,0. 2.2.4. x1. T. x, x. T. H. x2 (2.22). T. x1 , x 2. T. x3 , x4. ,. T. x 2r. x 2r , x 2r. u. T. ua. 1. (2.25). ur. 1. x. 1. 0,0 T. 1 s. xr. 0.1. s. 3. s 0.8, 0.5, 0.2. 0 1 s. s. if. 1. x r 0.1 x. x r 0.1 (2.25). 1 s otherwise Actor-Critic. rt. exp. (2.26). x xr 2. r. ,. r. ,. 2. x2 r. ( x) 2 2. v2 r. 2. 2 r. (2.26). r. x v r, r. x, x. Actor-Critic 1. x r ,0. (2.26) 0. 2. H. 2 2.2.4. H. 1.

(28) H. 2 Actor-Critic x. Actor. , , x, x. Critic. Actor-Critic. (2.27) 2. rt. exp. 2. 2 2. r. 2. 2. 2. x xr x 2 r. 2. r. x2 2. (2.27). v 2 r. Actor-Critic. 0. xr. , , x, x. 1. 0,0, x r ,0. Actor-Critic x, x. (2.26). 1. xr ,0. Actor-Critic. Actor-Critic , , x, x. 1. ((2.27. 0,0, xr ,0. )). 2.3.3 3. 1. Fig.2.6~2.8. 2. 5m. 1000. 1000 1. Fig.2.5, Fig.6 0. s. 0.8. s. (2.25). 10. s. 0.8. ua. 0.8. 0 5 Fig.2.7, Fig.2.8 s. 0.5. s s. 2 3. 0.5. s. s. 0.5. 0.8. Fig.2.9, Fig.2.10. 1 2 1, 2. (Fig.2.9). 0. 5[m]. (Fig.2.10). 1, 2 1. 2. 2 1. s. 0.5. 1.

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(31) Fig.2.9.. Comparison of control results of the angle among the three. Fig.2.10. Comparison of control results of the position among the three.

(32) 2.3.4 1 2 Table 2.2 1 2. Table 2.2. Results of robustness validation. Proposed Proposed method 1 method 2. Actor-Critic method. Maximum weight of the load. 2.10. 1.49. 0.98. Minimum weight of the load. 0.00. 0.00. 0.48. Maximum weight of the trolley. 23.05. 48.48. 23.75. Minimum weight of the trolley. 0.00. 0.00. 0.98. Maximum length of the pendulum. 1.33. 1.48. 0.95. Minimum length of the pendulum. 0.21. 0.01. 0.47. Maximum objective point. 5.24. 10.00. 5.40. Minimum objective point. 4.82. -10.00. 5.00. Maximum initial angle. 14.08. 30.00. 13.32. Minimum initial angle. -14.08. -30.00. -13.32.

(33) 2.3.5 H. 1 2 2. H. 2.4 1. 2 1. H H.

(34) H. H H H H H. H.

(35) L2. H. n. x. T. x, x, , x n 1 u g 0. xn. f x. x1 , x2,. , xn. x. T. g xu Rn. Ax B f x. 0 1 0 0 0 1 0 0 0 0 0 0. r. 0 0 ,. 1 0. r. x. g xu. 0 0. A. x. f,g. e. e r x. B 0 1.

(36) e. e, e,. ,e n. 1 T. Rn r. r, r,. ,r. f,g. Rn. u. u k. n 1 T. kn , k n 1 , , k1. T. g. 1. f. r. n. kTe. Rn. rn. n. u. en k i i 1,2,. k1e n. 1. k n 1e k n e. 0. n lim et t. f ,g. 0. u.

(37) H. H. rf. x Q. uh. e. k. ur. P. u. rt. Pt. rt.

(38) H k. Q T. 0 0. P. P. 1 0. Q. 0 1. 0 0. 0 0. 0. 0. kn. kn. 1. 0. 1. k2. k1 P. H. uh. 1 T e PB 8 2 H. uh.

(39) i 1,2,. n ,n. R. A ji b act j. j. w act j. ur greedy. ur. j 1,2, j. ,R.

(40) R. ur. act w act j bj. with. probabilit y 1. j 1 R. act w act j bj. ns. with. probabilit y. j 1. ns j I. b act j. A ji e i. 1. i 1. I. A ji. A ji e c act ji. act 2 ji. i 1. exp. act 2 ji. i. max b act , j. j 1,2,. ,R t. t. Rt. c act ji. 1. j. max. max th. ei. t. th. 0,1. th. R. R. R 1. 2. ns b act j.

(41) wRact c Riaxt. ei. act Ri. wc ,. wc 1. c. c. rt. Pv t. V t n. V t. rt. n. n 0. 0. V t. 1. V t. rt. V t 1. rt. rt. Pv t 1. Pv t. Pv t.

(42) j w cri j. J b. 1,2,. ,J. j. cri j. Pv t. Pv t. J. cri wcri j bj. j 1. b cri j. f tanh x. f tanh x. 1 exp 1 exp. 1 exp b tanh ei j. I. x x. i v cri ji e. 1. i v cri ji e. 1. i 1. 1. 1 exp. I i 1. I. j v cri ji. 1,2,. , J i 1,2,. ,I. i. j.

(43) w act j. act w. c act ji. act c. act ji. wcri j. cri v. act c. ,. act. ,. u. Pv wcri j. Pv v cri ji. Pv. r. 1 2 r 2. 1 2 r Pv 2. act. cri ,. u r c act ji act ji. cri w. v cri ji act w. act. u r w act j. cri w. ,. cri v. ,. cri c. ,. cri. r2 2. r. rt.

(44) H e L2. tf. t. G. L2 0 ,t f. t. H. e. sup. 2. t 2. L2. e. sup L2 0 ,t f. t. 2. t 2. H. H. H tf 0. eT Qedt. tf. Q. eT 0 Pe 0. 2. tf 0. T t. t. dt. t. PT. P. P. L2 tf. 2. e Q2. 0. 2. tf. 2. 0. e0. eT Qedt T t. t. dt. 0 2. e Q2. 2. 2 t 2. 0. Q.

(45) sup. e Q2 t 2. t. H. L2 0, t f. H. H. rf n. d kT e. f gu. n. en. rf n. xn f. d kT e. gu. kT e g u. e B1 u. 0 0. 1 0. 0 kn. 0 kn 1. gu d. u. e. 0 1. f. 0 0 0 k2. u. 0 0 , B1 1 k1. 0 0 0 g.

(46) u ur. ur. uh. uh. e. e B1 u. ur. u. u. u. V. ur uh. e. e B1. V. e T Pe. V. eT Pe. eT P e eT PB 1 eT P. T. ur. u. uh. u. eT Pe eT. uh. P e 2eT PB 1. 2eT PB 1. T. e Qe 2e PB guh. V. eT Qe eT Qe. g T e PB 4 2 g 2. 2. 2eT PBg. eT PB 2. g g. uh Pe. u. uh. u. eT Qe 2eT PB 1uh T. BT1. Pe. uh. u. eT Qe 2eT PB 1. V. T. u. T. 2e PB g. u. u 2 u. 2. g g. T u. 2. g g. u.

(47) eT Qe. V. 2. g g. T u. g g. 2. u. 0, t f. V tf V tf. 0,V 0. tf. V 0. 0. eT Qedt. g g. 2. 2 tf 0. T u. u. u. dt. dt. eT 0 Pe 0 tf 0. eT Qedt. eT 0 Pe 0. 2. g g. 2 tf 0. T u. H. 2. g g. H. e. u. g. 0 g min g min. g. g max. g. g max. g. 2. g max g min. 2. g g.

(48) u u. ur. u j. b. act j. 0. b. act j. j. 1. w act j w act j w act j. w D. act j. w act j. w act j w act j. w act j. if. w act j. w act j. D. otherwise w act j. D.

(49) mL. g r sin f. 4 L 3. g. 2 2. sin cos mc m. m cos 2 mc m. cos mc m 4 m cos 2 L 3 mc m mp. mc gr u. x x. x1 , x2. T. , r. H. L T.

(50) mc =1.0[kg] m p =0.1[kg] L =1.0[m]. [56] g r =9.8[m/ s ]. -45. 2. 30.0. ( -0.785[rad]). 0[rad/s]. r. 0.01. tf 0 tf ti. sin t. et dt t f et dt t f. ti. ti. tf. ti. tf. [17] [32]. k1 =5.0, k 2 =1.0, Q =diag{10.0, 10.0}, =0.3, g min =0.6, g max =1.5, I =2, J =5, I c =1.0, Pth =0.1,. =0.01,. =5.0,. =0.01, I th =0.01, =1.0,. =1,2, , J ). =0.001, =0.95,. cri w. =0.01,. cri v. Actor. th. =10.0,. =0.3, act c. c. =0.2,. =0.01,. act. , w cri , v criji ( i =1, , I ),( j j. =0.1, D =500.0, n s =[-10.0, 10.0] [-1.0, 1.0]. (3.50). R =1. =1,2, , R ). =0.01,. act w. 0.077. , c act , wact j ji. act ji. ( i =1, , I ),( j. (3.10). Fig.3.5. Table.3.1 Fig.3.5 Fig.3.7. TD. Fig.3.9. Fig.3.6. Fig.3.6. 0 5. Fig.3.8. Fig.3.8. Fig.3.11. Fig.3.10. Actor. Actor Fig.3.13. HTC. Fig.3.12. Actor. Actor. (. ). Fig.3.6 Fig.3.7. (RRLCS). 0. AFC ASFNCS HTC. H Actor Fig.3.8 Fig.3.9. TD. Fig.3.10 2. HTC HTC. 0. Actor.

(51) Actor. 2. NN. Table.2.1 ASFNCS. AFC. Fig.3.11. Fig.3.13. Actor. NN Actor Fig.3.11. Fig.3.11. Actor. Actor. Fig.3.12, Fig.3.13. 10. 3. 10. 2. 10. 3. 10. 4. 10. 3. 10. 3.

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(57) Albus CMAC(Cerebellar Model Articulation Controller)[54] CMAC. (LUT) (NN). [50]. Almeida. CMAC. CMAC(PCMAC). [74]. CMAC (. LUT CMAC. PCMAC ). PCMAC (RPCSGD). LUT Lu. [56]. PCMAC LUT LUT. (RRLCS). [43]. RRLCS. H NN Lu PCMAC. LUT. (CP) PCMAC RRLCS. NN.

(58) (. ) (. ) CP (CPRCS) RRLCS[43] RPCSGD[56]. n. xn xn. x. f x. g xu x, x, , x n. x. n f ,g. (4.1) 1 T. T. x1, x2 , , xn g 0) u r r, r , , r n 1. (. x e r x. u k. kn , kn 1,. g. , k1. T. f ,g. 0. 1. f. r. n. kT e. T. r. n. r. n. (3.1). en. k1e n 1. kn 1e kn e 0. (4.3). k i ( i =1,2, , n ) (3.3) (3.2). (3.3). f ,g. CP =1,2, , n ). CP. (. CP). lim et t. 0. u. Ii (i. Fig.3.1 CP Fig.4.1 (Receptive-Field Space). (Parameter Space). 1.

(59) CP. pj. bj. I1. p2. b2. w2. uc. dj. assoc In. Fig.4.1.. b5. p5. b7. p7. w5 w7. Structure of the cerebellar perceptron improved model. (Association Space) CP. cij bj pj. wj. uc. CP. CP. Ii dj. j. cij. i. (4.4) n. dj. Ii. cij ,. j. 1,2,. ,m. (4.4). i 1. m. (. dj. ) ((4.5). ). dj. a a m (a. ). uc. (4.4). ei. CP 0 0. 1. Ii cij (4.4).

(60) b assoc j. j. b assoc j. exp. 2. ,. assoc 2 ij. i 1. cijassoc ,. cijassoc. Ii. n. assoc ij. j 1,2,. ,a. (4.5). j assoc. c. i b assoc j. assoc assoc c11assoc, , c nassoc , c nassoc , c1assoc , , c na a 1 , c12 , 2 , assoc 11. , ,. assoc n1. assoc 12. ,. , ,. assoc n2. , ,. assoc 1a. , ,. T. assoc T na. (4.6) (4.7). j p assoc j. p assoc j assoc p0assoc , j , p1, j ,. p0assoc ,j. p1assoc , j I1. pnassoc 1,2, , j In , j. ,a. (4.8). , pnassoc ,j. T. assoc piassoc , piassoc , i 0,1, , a ,1 , pi , 2 , ,a. pi. (4.9). uc. CP. uc T. b. b T Pw. T. w. bT P. b1assoc b2assoc. baassoc. T. b Ra 1. (4.12).

(61) P. p1assoc 0. 0 p. 0. assoc 2. 0 0. w. Ra. P. a. (4.13). p aassoc. 0. w1assoc w2assoc. waassoc. T. w Ra 1. (4.14). assoc assoc b assoc , p j , w j ( j =1,2, , a ) j. b ,P,w. 1. Fig.4.1. Fig.1. b1 , p1 , w1. (4.12) assoc 1 assoc 3. p2 , p. p. w. assoc 2. a =3 b2 , b5 , b7 p2 , p5 , p7 w2 , w5 , w7 assoc b5 , b3assoc b7 (4.13) b1assoc b2 , b2 P assoc a sso c p7 (4.13) w5 , w1 w2 , w2 w u c (4.10). b p5 , p3assoc. w7. uc. b2 p2 w2. b5 p5 w5. b7 p7 w7. CP CP. d min. d min. min d j ,. d min. wm. ,m d th. d th. 0, c i m. 1. p 0, m pre , i. j 1,2,. 1. 1. p 0pre , p i , m. p0pre , pipre ( i =1,2, , n ). Ii ,. i m 1. 1. p ipre. pre i. m. m. m 1.

(62) Sj. ( j =1,2, , m ). Sj. 1.0. S j t exp 1 S j t 2 exp. Sj t 1 1. ,. 2. if not associate if associate 2 1 Sj t. j 1,2,. ,m. (4.18). 0. Sj S th. S th. j. m a m. (4.18) a. r. a. uc [40]. [56]. [40]. (4.18). [56]. (CPRCS). Fig.4.2. Plant (RC). CP. u. (4.2) CP. Plant. u. RC. uc. CPRCS. CP. u. u uc u r ur. RC. s. s. en1. k1e n. k i ( i =1,2, , n ) 4. ur. 2. 1 3. s. 2. t. kn e 0. d. (4.20).

(63) Fig.4.2.. A cerebellar perceptron-based robust control system. uc. CP. u. u T. uc. ,w. w. ,w. CP T. uc ,w. uc. w. ,w. u~ u. u. uc T. T w w T ~ ~ w ~Tw ~Tw. ~. ~ ,w. w. w. ~. CP.

(64) ~. ~ DTc ~c DT ~ DT0 p 0 n. DTc ~c DT ~. ~ h DTn p n. ~ h DTi p i. i 0. ~ c. h. ~. ~. ~. 1. a. c 1. c. 1. c c. a. 2. a. 2. pi. p i ( i =0,1, , n ). T. 2. c. Di. pi. a. 1. D. (4.25). ~. 2. Dc. ~ , p i. c, ~. c. pi. pi. ,i. 0,1, , n. pi pi. (4.24). u~. T. ~ ~c T D w ~ T D w w c. n. ~T D w p i i. i 0. ~Tw ~. hT w. s. (4.20). st (4.19). (4.2). k1e n. 1. f. g uc. r. n. gu g. 0. xn. k1e n. 1. kne. uc u r 0. g. g max g g max (4.23). ur. (4.32). st. CP. kn e. (4.1). xn (4.31). en. (4.1) (4.30). g max. g. CP (4.33). g. uc.

(65) st. T. g max. n. ~ ~c T D w ~ T D w w c. ~T D w p i i. i 0. [31],[56]. V w,. c. ,. V. ,. w. ~T ~. ~T p ~ p i i. n i 0. c. i. ,n). i ( i =0,1,. ss. ~c T ~c. ~Tw ~ w. 1 s2 2. ~ cT ~ c. ~Tw ~ w w. ~T ~. n i 0. c. ~T p ~ p i i i. (4.34). V. ~ w. ~ T sg max w. ~c T sg max D w c. w. c. ~ T sg max D w n. ~ ~ p i. ~ T sg max D w p i i. i 0. i. ur. (4.21). g max , g max. 0. g. g max. [17],[43]. w. ~c. ~ w. w. s. sg max. ur. ur.

(66) c. ~ c. c. ~ p i. pi. Dc w. s. ~. (4.39) ~(4.42). s. i. D w s. D i w,. i. 0,1,. ,n. (4.37). V. s. ur. ur. (4.21). V. 4. s. 1 4. 2 s2 2. 1 2. 2. s 2. s2 2. 1 2. 2. 1 2. 2. 2. 2. tf. 0, t f. V tf V tf. s2. 1 2. V 0. tf 0. s 2 dt. 1 2. 2. tf 0. 2. dt. 0. 1 2 V 0 [17-18],[31],[56]. tf 0. s 2 dt V 0. 1 2. 2. tf 0. 2. dt s. tf. 0.

(67) 3. x. u. r (CPRCS). H. (RRLCS)[43] PCMAC (RPCSGD)[56]. mc =1.0[kg] m p =0.1[kg] L =1.0[m] g r =9.8[m/ s 2 ]. [56] -45. ( -0.785[rad]). 0[rad/s]. r. 0.01. r. 0.5 sin t. 0.5 cos 2t (ref 2). 30.0. sin t (ref 1). 2. n. d th. k2. p 2pre. 1. w. c. pre. S th. 2. 0. p. i 1. a p1pre. pre 0. g max. 2. m. a. cij. c i1. ci 2. i. Ii. Ii i. r. k1. e. ci 0. i 1. sin t. Table 4.1. (ref 1). Fig.4.3. e. Fig.4.4. Fig.4.5. Fig.4.6 Fig.4.3 Fig.4.3 0.02 (CPRCS) RRLCS RPCSGD. 0 Table.4.1.

(68) RRLCS. RPCSGD CP. m. w c. pi i. p0. w. p0. 10. 3. 10. 3. 10. 3. 10. 4. 10. 4. 10. 3.

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(73) r. 0.5 sin t. Table 4.2. 0.5 cos 2t. (ref 2). Fig.4.12. e. Fig.4.13. Fig.4.14. Fig.4.13 Fig.4.12 0 (CPRCS) RRLCS. RPCSGD. Table.4.2. RRLCS CP 0 m. w c. RPCSGD.

(74) pi i. dj. 10. 3. 10. 2. 10. 2. 10. 4. 10. 3. 10. 3.

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(80) 4. CMAC. 2. 1. 1. 1. 1 (FEL)[50-53]. FEL (Conventional Feedback Controller (NN). (Multi Layer Perceptron NN. 1. MLP). Feedforward Controller NNFC). CFC). (Neural Network [51] CFC. CFC. 0. 2 [76]. 3 2. FEL PID. [43,51-52]. Sabahi. [51]. NNFC NN. H (ASFNN)[31-35] [43]. [52] Sabahi. Farivar. (RRLCS). Farivar. CFC.

(81) [53]. Topalov. CFC. PD. NNFC. MLP (NASCS). [53]. [51-52] NNFC. 3. (CP). FEL NNFC. CP. (AFCPCS) CFC FEL. NNFC. CP. RRLCS[43]. NASCS[53]. n. xn xn. x. n f ,g. f x x. g xu ,x n. x, x,. g. (. 1 T. u R r. 0). x e r x 0 (10). x1 , x2 ,. Fig.5.1. f. f. 1. r. uc x. x x. r. f uc. f f e. 1. r. 0. Fig.1. r. r, r,. , xn. T. ,r. n 1 T.

(82) Fig.5.1.. r x. Structure of feedback error learning. e. r. (NNFC) u NNFC. NN. r. (CFC) u CFC. x. [51]. u. (Plant). u u NNFC uCFC u NNFC. u. E NN. 1 u 2. u NNFC. 2. w. E w. w. u NNFC w u. u NNFC. u. u NNFC u NNFC. 0. uCFC u. u NNFC. u CFC. u CFC. w. u NNFC u CFC w. (5.3). 0. u. u NNFC.

(83) [50]. NNFC. MAS. (CP) (i. 1,2,. ,z). Fig.5.2. (Input Layer). Ii. (Fig.5.2. bj pj. qj. (Hidden Layer) ). wj. (Output Layer). uc. CP. Ii. j. Ii. z. qj. exp (. ). cij. ,. 2 ij. i 1. m. qj 2. cij. j 1,2,. ,m. j. i. 2 ij. a(a. m). Ii. b assoc j. p assoc j. I1. qj. assoc In. p1. b1. p2. b2. p3. b3. p4. b4. p5. b5. p6. b6. p7. b7. pm. bm. w12. u1. w15 w17 wK 2 wK 5. wK 7. Fig.5.2. Structure of the cerebellar perceptron improved model. uK.

(84) b assoc j. exp. 2. ,. assoc 2 ij. i 1. p assoc j. ciassoc j. Ii. z. p0assoc p1assoc ,j , j I1. b assoc j. j. 1,2,. p zassoc ,j Iz , j. ,a. 1,2, , a. j (5.6). (5.7). p assoc j. Ii , ciassoc j. assoc 2 ij. j p. i. assoc 0, j. assoc 1, j. ,p. ,. ,p. assoc z, j. assoc CP. wkassoc b assoc j j. uc. p assoc j a. uk. wkassoc b assoc j j. p assoc , j. k 1,2,. ,K. (5.8). j 1. wkassoc j. K 2. wkassoc b assoc j j. k. j assoc kj. w. CP. b. assoc j. p assoc j. p assoc j. p assoc j. CP. CP. (5.8). CP CP. b1 , b2 , , bm. bmax bmax bth. p assoc j. max b j , j. bth , bth. 0,1. j 1,2,. ,m.

(85) wm. p0 , m pre i. pre. pre. 0, ci m. 1. Ii ,. 1. p0pre , pi ,m. 1. pre i. i m 1. pipre. 1. ( i =1,2, , z ). , p0 , pi. m. ( j =1,2, , m ). m. Sj. assoc. 3. unnec assoc. a. unnec. Sj. 1.0. Sj t Sj t 1. 2 exp. S j t exp. 1. 1 Sj t. 2. Sj t 1. ,. if. bj. assoc. if. bj. unnec. j. 1,2,. ,m. otherwise assoc. 2. unnec. Sj. j. unnec. M1. Sth cif ,. f 2 i. unnec. cij. d I. d d. j (M2 ). cij cif ,. min j. bj. ,. M1 N2. ij. cif. cij 2 ij. cij ,. ,m. CP. M2 2 ij. 2 f 2 i. Sj 1. j 1,2,. assoc. i 1. d th. cij. m 1. 1.0. m.

(86) (5.11). assoc. m. a. unnec. 2a. (m. 2a ). assoc. (AFCPRCS) Fig.5.3. CFC. ur. (RC). CP. CP. RC. u. uc. u RC. uc. ur. RC 0. CP AFCPRCS. ur. ur 4. ur. 2. 1 3. s. s. Fig.5.3.. Auto-fusion cerebellar perceptron-based robust control system.

(87) s. en. 1. k1e n. t. 2. kn e 0. d. k i ( i =1,2, , n ). (AFCPRCS) 0. ur. 0. (5.16). CP. cijassoc. w. piassoc. CP. ,. ,. i. ( i =0,1, , n ). 0. uc s wkjassoc uc. c. assoc ij. i. uc piassoc. (5.18). s. cijassoc uc. assoc ij. c. s. s. wkjassoc. ,. RC. (5.17). ur. w. ur. RC. s. s s.

(88) 3 3. (CPRCS). PD. (NASCS)[51] 2 -45. mc =1.0[kg]. ( -0.785[rad]). g r =9.8[m/ s 2 ]. 0. r. 0.01. L =1.0[m]. m p =0.1[kg]. 30.0. sin t (ref 1). r. 0.5 sin t. 0.5 cos 2t (ref 2). 2. (3.49),(3.50) (. ) (. 5 30 ). 2. n =2, a =3, k1 =5.0, k 2 =10.0, bth =0.2, =1.0, p 2pre =1.5,. p. pre 0 ,. w. pre , 1. p. 1. =35.0,. p. pre 2 ,. c. w,. =0.05,. 2. =1.0, c. =0.05, S th =0.1, d th =0.5,. =1.0,. ,. ,. 0. ,. 0 1. ,. =1.0,. 1. =1.0,. 2. pre i. =1.0,. =0.2, p. pre 0. =0.5, p1pre. =0.3. 2. u if u if. m = a =3. CP. cij. I i ( i =1,2). Ii. ri. 1. (5.10). ci 0 =0.0, ci1 =0.5, ci 2 =-0.5( i =1,2). CP.

(89) r. sin t. Table.5.1. Fig.5.4. e. Fig.5.5 Fig.5.7 ( ((5.5). ). ). Fig.5.6. CP. m. Fig.5.5. RC. Fig.5.8. Fig.5.9. 3. w. Fig.5.10. c. Fig.5.11. pi ( i. 25~30. Fig.5.12. 0,1,2 ). sin t. Fig.5.4. Fig.5.5 0.04. 0. AFCPRCS(. ). CPRCS. NACSC. 0 Fig.5.7. 12. CP. Fig.5.5. Fig.5.6. Table.5.1. CPRCS. (AFCPRCS) NASCS CPRCS. 0. Table.1 CPRCS CPRCS Fig.5.8. 17. 2a 1. 2. a 3 1. 2a 1 5. 3. CPRCS. 3. 19. 1 4 NACSC. MLP. 20 NN.

(90) Fig.5.10. Fig.5.8 5 5. 2. 5. 10. 3. 10. 3. 10. 2. 10. 4. 10. 4. 10. 4.

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(95) r. 0.5 sin t. 0.5 cos 2t. Table.5.2. Fig.5.13. e. Fig.5.14 25~30. Fig.5.17. Fig.5.18. (. 3. ((5.5). w. CP. m. ). Fig.5.15. ). Fig.5.16. RC. Fig.5.19 Fig.5.20. c. Fig.5.21. pi ( i. Fig.5.22. 0.5 sin t. Fig.5.13. 0,1,2 ). 0.5 cos 2t CPRCS. NASCS Fig.5.14. Fig.5.14 0 ). CPRCS. NACSC. 0.5 sin t. 0.4 AFCPRCS(. Fig.5.16. 0.5 cos 2t. -1. 20. CP. Fig.5.15. Table.5.2. CPRCS. (AFCPRCS) NASCS CPRCS. 0. Table.4.2 CPRCS CPRCS Fig.5.17. 17. 2a 1. 2. a 3 1. 2a 1 5. 3. CPRCS. 1. 3 CPRCS. CP. ei CP. Ii. CPRCS. r. (AFCPRCS) NACSC 20. MLP.

(96) NN Fig.5.19~Fig.5.21 Fig.5.17. 5 5. 24. 4. 1 5. 10. 3. 10. 3. 10. 2. 10. 4. 10. 4. 10. 3.

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(101) 2 CP. CP. sin t 0.087 sin t. 5. sin t. 0.5 sin t. 0.5 cos 2t. 1. sin t 0.5 sin t. 0.5 cos 2t 2.

(102) 3~5. (SISO) (MIMO) 4 (CPRCS). SISO. MIMO. 5. (AFCPRCS). MIMO. (. ). (MAS). [78-96] MAS MAS. [78,88,95] Hou. NN (Decentralized. Robust Adaptive Control System DRACS) [78]. NN. MAS. AFCPRCS. MIMO. 6 DRACS MAS. 1. CPRCS MAS CPRCS. 2.

(103) MAS 1 CPRCS MAS. G. V,E. n Ni. Ni. E. v j V : v j , vi xi. V. v1 , v2 , vi. vi. i. V V. E. , vn. i. Ni A. A. L. aij D. vi. 1. vj. Ni. 0. vj. Ni. D. aij. i. D diag d1 , d 2 , , d n n. di. aij. j 1. L. l ij. A. L D A i. j. l ij. D.

(104) n. MAS. xi xi. T. xi1 , xi 2 , , x1m. f i xi. 1. gi xi ui m. i. fi , gi. gi. (. Xj. (Fig6.1. 0 ) ui. aij. 1. ). i. MAS. ui. lim xi t. xj t. t. 1 n xi. t. n. i, j 1,2,. ,n. aij. a ji xi 0 ( i =1,2, , n ) T , n 1, 2 ,. i, j. G. xi 0. 0,. xi 0. i 1. 0. 2. 1 1. (6.5) (6.6). MAS (AFCPCS). Fig.6.1. MAS. i. i. CFC FCC. u. (FCC). f i. CP. CP. u ic. CP. ui. ((6.4) ). ui. uic uif. FCC. ui. u if. 0.

(105) Fig.6.1.. Structure of the proposed system for i th agent T. w iassoc b iassoc p iassoc. u ic u. 4. f i. 2. 1 3. ei. ei n. ei. lij x j. (6.10). j 1. u ic. i. u if. fi g i. uic. fi g i. u if. xi. 0 w. i. 0. assoc i. b iassoc. p iassoc b iassoc. p iassoc. Iz. xiz.

(106) (5.4) 0. u if. 0. u. CP. (6.9) f i. FCC. FCC. (6.10). 0. ei. w iassoc. c. w. assoc i. c. u ic ei w iassoc u ic c iassoc u ic. assoc i. p. assoc i. assoc i. i. ei. ei. u ic ei p iassoc assoc 2 i. c iassoc w. ei. c. u if. i. i. n.

(107) MIMO. 6. 2. d xi1 t dt xi 2 t. xi 2 t sin ki1 xi1 t. ui. xi1 t cos ki 2 xi22 t. k i1 , k i 2 (AFCPCS). NN (DRACS)[78] MAS. xi MAS. 2. x i1. 1. 2. xi 2. 2. x1ave. xi 2. x2ave. 1 n. (distance error) n. x. xi. i 1. xie. xie1. 1 n. x1ave MAS. xie2. xi1. n. xi1 , i 1. x2ave n. xi 2 i 1. (consensus error). xe. n. xie. i 1. (6.15). (6.7) MAS. 6. (n. 6).

(108) 0.01[s]. 10.0[s]. (DRACS). [77]. k i1 , k i 2. k11, k12 k41, k42 x11, x12. 0.6,0.3 , k21, k22. 0.6,0.4 , k31, k32. 10.0, 11.0 , k51, k52 6.0,0.0 , x21, x22. x41, x42. 7.0, 5.0. 10.0,11.0 , k61, k62. 3.0,3 3 , x31, x32. 6.0,0.0 , x51, x52. 3.0,3 3. 3.0, 3 3 , x61, x62. (6.6). (0,0). x. e. 0.01,10.0. 3.0, 3 3 MAS. 0.4. xe. 45. 0.1%. A. Fig.6.2. 0.0 0.1 0.0 0.0 0.0 0.6 0.1 0.0 0.2 0.0 0.0 0.0 A. 0.0 0.2 0.0 0.3 0.0 0.0 0.0 0.0 0.3 0.0 0.4 0.0 0.0 0.0 0.0 0.4 0.0 0.5 0.6 0.0 0.0 0.0 0.5 0.0 6.

(109) a =3, bth =0.3, 1. =0.01,. =0.1,. 2. pre i. =0.01, S th =0.1, d th =1.0,. c =0.01,. =0.01,. 0 =0.03,. 1 =0.02,. pre. =1.0, p0 2 =0.01,. m = a =3 cij ci 0 =0.0, ci1 =5.0, ci 2 =-5.0( i =1,2) NN I z ( z =1,2) I z xiz. pre. pre. =0.01, p1. =0.1, p 2. =0.3. CP. =0.15,. w. (4.10) CP NN. (DRACS) 36. [78]. Fig.6.3. (AFCPCS). Fig.6.4. Fig.6.5. Fig.6.6. x1. Fig.6.5,Fig.6.6. x2. Fig.6.7 Fig.6.8. Fig.6.9. Fig.6.10 Fig.6.11. Fig.6.6. MAS. [0:0.4]. DRACS. Fig.6.7. DRACS 0.2 Fig.6.10 0.6. DRACS MAS. 0.4. DRACS MAS. 3 8. Fig.6.11. 0. DRACS DRACS.

(110) Fig.6.12. x1. Fig.6.13. x2. Fig.6.14. x1 x2. Fig.6.15 Fig.6.16. Fig.6.17. w. Fig.6.18. c. Fig.6.19 Fig.6.20. p0. Fig.6.21. p1. Fig.6.22. p2. x1 , x 2 x1 , x 2. c. ph h. 0,1,2.

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