Recurrent Neural Network Based Fuzzy Inference System for Identification and Control of Dynamic Plants

Transcription

1 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 Recurrent Neura Network Based Fuzzy Inference System for Identfcaton and Contro of Dynamc Pants Rahb Hdayat Abyev Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 Abstract- Ths paper presents the deveopment of recurrent neura network based fuzzy nference system for dentfcaton and contro of dynamc nonnear pant. The structure and agorthms of fuzzy system based on recurrent neura network are descrbed. To tran unknown parameters of the system the supervsed earnng agorthm s used. As a resut of earnng, the rues of neuro-fuzzy system are formed. The neuro-fuzzy system s used for the dentfcaton and contro of nonnear dynamc pant. The smuaton resuts of dentfcaton and contro systems based on recurrent neuro-fuzzy network are compared wth the smuaton resuts of other neura systems. It s found that the recurrent neuro-fuzzy based system has better performance than the others. eywords- Fuzzy ogc, neura network, neuro-fuzzy system, contro system I. INTRODUCTION UZZY systems have found a number of practca F appcatons n dentfcaton, contro, predcton and dagnosng. These systems are thoroughy deang wth defned, uncertan systems, can mode the quatve aspects of human knowedge and reasonng process [-5]. Tradtonay, to deveop a fuzzy system, human experts often carry out the generaton of IF-THEN rues by expressng ther knowedge. In case of compcated processes t s dffcut for human experts to test a the nput-output data, to fnd necessary rues for fuzzy controer. To sove ths probem and smpfy the generatng of IF-THEN rues, severa approaches have been apped [-5]. Nowadays for ths purpose the use of neura networks take mportance. Usng neura network structure and ts earnng abtes the constructon of fuzzy system s consdered. The ntegraton of fuzzy system and neura network aow to construct computatonay effcent hardware and software products. It s connected wth the capabtes that they posses. Fuzzy systems provde powerfu framework for representaton of expert knowedge, neura network provde earnng capabtes that ncrease the fexbty, adaptabty of the system. The combnaton of neura networks wth fuzzy knowedge base heps to reduce the searchng space and tme for achevng optma souton. In Manuscrpt receved Juy, 003. Ths work was supported by the Near East Unversty, efkosha, TRNC, Turkey. Rahb H. Abyev s wth the Department of Computer Engneerng, Near East Unversty, Mersn-0, TRNC, Turkey (e-ma rahb@neu.edu.tr). genera, there are two ways about deveopment of systems based on combnaton of fuzzy system and neura network. The neura network s represented by fuzzy parameters whch s known as fuzzy neura network, and the functonaty of fuzzy system s reazed by neura network structure, whch s known as neuro-fuzzy or neura fuzzy systems. Durng constructon of neuro-fuzzy systems the foowng requrements are necessary. These are fndng the optma vaues of neura network parameters and the necessary number of optmum rues. Neuro-fuzzy system combnes the earnng capabtes of neura networks wth the ngustc rue nterpretaton of fuzzy nference systems. The synthess of neuro-fuzzy nference system for controer ncudes the generaton of knowedge base rues that have IF-THEN form. Here, the probem conssts n the optma defnton of the premse and consequent part of fuzzy IF-THEN rues for controer through the tranng capabty of neura networks, evauatng the error response of the system. There are two types of IF-THEN rues used n fuzzy systems. The frst one conssts of rues, whose antecedents and consequents parts utze fuzzy vaues and t s caed as Mamdan-type fuzzy rues. IF x s A and x THEN y s C s A and and x n s A Here x and y are nput and output varabes of system, respectvey, =.. s the number of rues, = n s number of nput sgnas. A and C are nput and output fuzzy sets, respectvey. The second type fuzzy system uses the rue base that has fuzzy antecedent and crsp consequent parts. IF x s A THEN y and x = b n s A + a x and and x n s A Ths type of rue s Takag-Sugeno-anag (TS) type fuzzy IF-THEN rues. The second type of fuzzy system approxmates nonnear system wth near systems. Ths type of systems empoys the other types of fuzzy reasonng mechansm. n n () () Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

2 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 Man probem n neura systems s ther fast earnng. To mprove ths characterstc severa approaches has been proposed. Severa nvestgatons have been made n [6-8] by usng mutayer perceptron, rada based functon neura networks, sef organzed maps. But dsadvantages of these works are not suffcent earnng speed of neura networks. The combnaton of neura network wth fuzzy system aows to ncrease the earnng speed. For earnng of parameters of such systems the supervsed agorthms are wdey used. It has good speed, and convergence. One of such agorthms s the back-propagaton agorthm. Back-propagaton agorthm aows to mnmze error functon very fast. In the paper the supervsed agorthm s apped for tranng neuro-fuzzy system coeffcents. Dfferent neuro-fuzzy structures are deveoped for sovng dentfcaton and contro probems [,5]. In [9] usng feedforward neura network the deveopment of adaptve neuro-fuzzy nference system (ANFIS) s presented. The ANFIS structure mpements TS type fuzzy system n a fve ayers network structure. Usng back- propagaton and east square agorthms the earnng of neuro-fuzzy system s carred out. In [0,] neura fuzzy controer NEFCON based on archtecture of the generc fuzzy perceptron descrbed. For earnng of the network parameters the fuzzy error backpropagaton agorthm s used. In [] a tranng procedure wth varabe system structure approach for fuzzy nference system s presented. The tranng dynamcs and stabty of the system s anayzed, the method for creatng stabzng forces on the tranng dynamcs of neuro-fuzzy system s proposed. In [3,4] the mut-ayer feedforward neura network s represented by fuzzy numbers for nputs, targets and connecton weghts. The earnng agorthm of fuzzy neura network s descrbed. In [5] usng α- eve procedure the tranng of fuzzy feedforward neura network s consdered. In [6-7] the fuzzy neura network s apped for contro of technoogca processes. As a mode of fuzzy neuron the mnmum operaton of weghted nput sgnas s used. Trapezod fuzzy numbers that are characterzed by four parameters represents the weght coeffcents of network. Usng α cut and nterva arthmetc the tranng of network parameters s carred out. Some of neuro-fuzzy systems have been deveoped by usng recurrent neura network. In [9] the concept of fuzzy system based on recurrent network s proposed. In [0] recurrent fuzzy network s used for nonnear modeng. The operaton prncpe of ths network s smar rada based functon network. Recurrent seforganzed neura-fuzzy nference system s represented. For earnng of networks parameters the supervsed earnng agorthm s used. In [] TS-type recurrent neuro-fuzzy neura network (TRFN) s deveoped. The outputs of fourth ayer are used for feedback connecton. The earnng probems TRFN by usng supervsed agorthm and genetc agorthm are presented. In [3,4] usng recurrent fuzzy neura network the constructon of controer for contro dynamc pant are consdered. The nterva arthmetc s used to tran the parameters of network. In ths paper the deveopment of fuzzy nference system based on recurrent neura network for dentfcaton and contro of dynamc pants s consdered. II. RECURRENT NEURO-FUZZY INFERENCE SYSTEM Assume that nput sgnas apped to the network at tme k are X(k). Output sgnas of the network are U(k). The output of neuro-fuzzy system based on feedforward neura network s determned by the foowng equaton. U(k)=F(X(k), M(k), M(k)) (3) Here X(k) and U(k) are externa nput sgnas and network output sgnas correspondngy. For Mamdan type fuzzy rues M(k) are membershp functons of the parameters of premse parts - between nput and hdden ayers and M(k) are membershp functons of the parameters of consequent part - between hdden and output ayers, respectvey. For Gaussan type membershp functon M(k) and M(k) depends on two parameters M(k)=G(C(k), Ω(k)), M(k)=G(C(k), Ω(k)). Here C(k), Ω(k) are centers and wdths of membershp functons between nput and hdden ayer, C(k), Ω(k) are centers and wdths of membershp functons between hdden and output ayers, respectvey. G s Gaussan functon. For TS type rues the vaues of M(k) are crsp numbers and they are descrbed ony by one parameters, that s C(k). In ths paper the structure of neuro-fuzzy system based on recurrent neura network s accepted as foows U(k)=F(X(k),U(k-),U(k-),,U(k-D), M(k), M(k)) (4) As shown the nputs of recurrent neura network are formed by the externa nput sgna X(k) and one-, two-,, D- step deayed output sgnas U(k-), U(k-),,U(k-D) of network. A. Archtecture of Recurrent Neuro-Fuzzy System In fgure the structure of neuro-fuzzy system based on recurrent neura network s shown. The nput sgnas apped to the network at tme k are x (k) (=..N) and output sgna of the network are u(k). N s number of neurons n the nput ayer. d s deay (d=..d). In frst ayer the number of nodes are equa to the sum of externa nputs and one-,two-,, D-step deayed output sgnas. In second ayer each node corresponds to one ngustc term. For each nput sgna enterng the system the membershp degree to whch nput vaue beongs to a fuzzy set s cacuated. To descrbe ngustc terms the Gaussan membershp functon s used. ( x c ) σ µ ( x ) = e =..n, =..J (5) Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

3 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 x R c x u(-d) R c u u u(-) R c u Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 ( u c+ n, ) σ+ n, µ ( u ) = e =..D, =J+..J+P (6) Here u =u(-). Here c and σ are the center and wdth of the Gaussan membershp functon of the -th term of -th nput varabe, respectvey. n s number of externa nput sgnas. J s s number of ngustc terms for externa nput sgna. P s number of ngustc terms for one-, two-,, D deayed output sgna of network. In the thrd ayer the numbers of nodes correspond to the number of rues. Each node represents one fuzzy ogc rue. Here to cacuate the vaues of output sgnas of the ayer AND (mn) operaton s used µ = µ ( r ), =.., =..J+P (7) z - z -d Here r ={x,..,x n,u,,u D }, I=,,n+D. Π s mn operaton. These µ sgnas are nput sgnas for the next ayer. Ths ayer s a consequent ayer. In ths fourth ayer the output sgnas of prevous ayer are mutped to the weght coeffcents of network. Weght coeffcents of neuro-fuzzy system are represented by fuzzy set of output varabes. They are descrbed by Gaussan functon. If as a defuzzfcaton operaton we use oca mean of maxmum then ony the center of Gaussan functon s used n the next ayer for defuzzfcaton. In ths case durng deveopment of contro system the wdth of Gaussan functon s not used. In formua Fgure. Structure of recurrent neuro-fuzzy nference system (8) the parameters c w represent the center of fuzzy coeffcents. Outputs of ffth ayer are cacuated as and u = µ * c, =.. (8) = u = µ = Usng the vaues of cacuated varabes, n the ast ayer the output of the fuzzy system s determned. u u u = = = µ * c = µ B. earnng of Recurrent Nneuro-Fuzzy System The unknown parameters of the system are c parameters of ast ayer and membershp functons of frst ayer of neurofuzzy system. To defne the accurate vaues of unknown parameters supervsed earnng agorthm s used. c here γ s earnng rate. (9) ( t + ) = c + η (0) c Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

4 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 E = m = ( u u d ) () d where u and u are current and desred outputs of the system, m s number of outputs. For gven case m=. = = ( u( t) u c c d ) The adustng of the membershp functons of nput ayer s carred out by correcton unknown parameters c and σ. The foowng formuas can be used for earnng these parameters. where Here c = c + γ, c σ = σ + γ, σ c σ = = = u( t) u c σ d, = c u = = ( x c ) µ ( x ) f node ( ) σ x = s connected to rue node c 0, otherwse ( x c ) µ ( x ) f node 3 σ ( x ) = s connected to rue node σ 0, otherwse µ () (3) (4) Usng (0) - (4) the earnng of the parameters of recurrent neuro-fuzzy system s carred out. III. SIMUATIONS OF RECURRENT NEURO-FUZZY INFERENCE SYSTEMS A. Identfcaton of Non-near Systems The dentfcaton probem s fndng reaton between nput and output of the system. Here the recurrent neuro-fuzzy nference system (RNFIS) s used for modeng dynamc pant. The nputs of dynamc pant are externa nput sgnas, ts one-,, d - step deayed vaues and one-, two-,,d o - step deayed outputs of the pant. Output of the system s determned by the foowng equaton. y(k)=f(u(k),u(k-),,u(k-d ), y(k-),y(k-),,y(k-d o )) (5) In fgure the structure of dentfcaton scheme s shown. u(k) z -,,z -d Pant z -,,z -d o RNFIS Fgure.. Identfcaton scheme y(k) y n (k) e(k) The probem s to fnd such vaues of parameters of RNFIS by usng them n the system for a nput vaues of u(k) the dfference between y(k) and y n (k) w be mnmum. Here y(k) s pant output, y n (k) s output of neuro-fuzzy system. As an exampe a second order nonnear pant that has been dscussed n [5] s consdered. The process s descrbed by the foowng dfference equaton. y( k ) y( k )( y( k ) 0.5) y ( k) = + u( k) (6) ( + y( k ) y( k ) ) Here y(k-), y(k-) are one- and two- step deayed output of the dynamc pant, u(k) s nput sgna. As a nput sgna for the pant the snusoda sgna u(k)=sn(πk/0) s gven. Input sgnas at the same tme are apped to the pant and RNFIS nputs. On the output of the pant the dfference between pant output and RNFIS output s determned e(k)=y(k)-y n (k). If the vaue of error s not acceptabe mnmum vaue the tranng of RNFIS start. The tranng s contnued unt the vaue of error becomes ess than sma acceptabe vaue. After next nput sgna s gven to the system nput and earnng process s contnued. The tranng of RNFIS s carred out for 6000 and 000 data ponts. Durng smuaton the nta vaues of parameters of premse part c and σ are generated Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

5 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 randomy n the nterva [ 0, 0], parameters of consequent part c and σ - n the nterva [, ]. The tranng s carred out for sxteen and forty-eght rues. For ths reason the earnng of neuro-fuzzy system s performed for two cases. In the frst case, number of neurons n hdden ayer s sxteen, n the second case- forty-eght. RNFIS nput ncudes externa snusoda nput sgna and, current and one- step deayed output of the pant. As a resut of earnng the membershp functons of premse and consequent parts of RNFIS have been found. In fgure 3 the curves that descrbe dentfcaton resuts are shown. Here sod ne descrbes the output of the pant, dashed ne descrbes the output of the RNFIS. Ths fgure demonstrates on-ne tranng processes. After tranng obtaned RNFIS mode was tested by dfferent nput sgna. Fgure 4 demonstrate the test resuts of RNFIS when nput sgna s u(k)=sn(π*k/0)+cos(k/0). In tabe I the resuts of smuatons of dentfcaton usng RNFIS and neuro-fuzzy nference system based on feedforward network (NFIS) are gven. Tabe descrbes onne earnng and test resuts for dfferent amount of rues and dfferent number of teratons. To estmate effcency of RNFIS the sum of square of errors and CPU- tmes are taken. Sum of square errors are cacuated as J = k = (7) Here s number of sampes. The experments are carred out wth 6 and 48 rues. The and 000- earnng resuts are fxed. In on-ne earnng mode, because of feedback connecton the CPU tme n RNFIS s greater than n NFIS. The estmated sum of square errors of systems wth 48 rues for both networks,5 tmes ess than sum of square errors wth 6 rues. The test resuts demonstrate the effcency of the RNFIS for sovng dentfcaton of dynamc pant. The test s carred out for 300 teratons. Test resuts are taken for 6000 and 000 earnng teratons. Resuts of comparsons of RNFIS and NFIS dentfcatons show that n the same condton the vaue of sum of square errors for RNFIS system two tmes s ess than NFIS system. The ncrease of a number of rues from 6 to 48 aows to decrease sum of square errors for two three tmes. B. Neuro-Fuzzy Contro The RNFIS structure and earnng agorthms descrbed above s used for deveopment of controer to contro parameters of dynamc pant. In fgure 5 the structure of RNFIS based contro system s gven. The nputs for neurofuzzy controer are error and change of error. The coeffcent k u s used for scang output sgna of controer. Usng the vaues of error and change of error t s needed to determne such vaues of contro sgna by usng them n contro system the target characterstc of the system woud be provded. Fgure 3. earnng resuts of dentfcaton by usng recurrent neuro-fuzzy system. Sod ne s output of the pant, dashed ne output of the recurrent neuro-fuzzy system. Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

6 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 On ne earnng Test resuts Number of rues Fgure 4. Test resut TABE I RESUTS OF COMPARISON BETWEEN TWO IDENTIFIERS 300 Number of teraton Error k = NFIS CPU - tme Error k = RNFIS CPU - tme earnng resut 00 earnng resut earnng resut earnng resut Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

7 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 At frst stage the fuzzy parameters of RNFIS that has Gaussan form are generated. In RNFIS structure the frst ayer represents nput sgnas error, change of error and one step deayed output of neuro-fuzzy system, second ayer s used to represent membershp functons of fuzzy parameters of premse part. The thrd ayer represents the number of rues. Forth ayer represents membershp functons of parameters of consequent part. Ffth and sxth ayers reaze defuzzfcaton mechansm. Usng nput varabes error and change of error and RNFIS structure the generaton of IF-THEN rues for controer n cosed oop contro system s performed. The consequent part of rues ncudes contro sgna gven to the obect. To fnd assocaton u(k)=f(e(k),e (k),u(k-)) between nput and output varabes of the controer, the earnng of unknown parameters of neuro-fuzzy controer n cosed oop contro system s performed. For earnng of the unknown coeffcents of neuro-fuzzy controer the error between target characterstc of contro system and current output vaue of g(k) D e(k) e (k) earnng agorthm Neurofuzzy controer Fgure 5. Structure of RNFIS based contro system mpemented system (output of contro obect) = g( k) y( k) s used. For earnng controer coeffcents the above descrbed supervsed earnng agorthm s used. Usng earnng agorthm the vaues of weght coeffcents of neuro-fuzzy controer are determned. Exampe. The deveopment of RNFIS based contro system s carred out for controng dynamc pant that s descrbed by (6). Computer smuaton of RNFIS based contro system for dynamc pant (6) s carred out. The nta vaues of the parameters of membershp functons of second (c and σ) and fourth (c and σ) ayers are generated randomy, n the nterva [ 0, 0] and [, ] correspondngy. Durng earnng the vaues of parameters of premse (second ayer) and consequent parts (fourth ayer) are adusted. In fgure 6 the curve that descrbes the earnng processes of contro system for dfferent vaues of set-pont sgnas s gven. k u Pant y(k) Fgure 6. earnng curve of tme response characterstc of contro system for dfferent vaues of set-pont sgna. Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

8 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 As a resut of earnng correspondng vaues of coeffcents of recurrent neuro-fuzzy system are determned. Smuaton resuts of RNFIS based contro system s compared wth the smuaton resuts of NFIS and RNN (recurrent neura network) based contro systems. In fgure 7 resuts of comparatve estmaton of tme response characterstcs of contro systems based on RNFIS, NFIS, and RNN are gven. Number of rues are 6. The resuts of smuaton of contro system based on RNFIS shows that the vaue of statc error of tme response characterstcs s absent (zero), transent overshoot s aso absent. The settng tme of system wth RNFIS based controer s ess than others. The resuts of smuaton and expermenta anayss of contro system wth RNFIS shows that t has better tme response characterstc than others. In tabe II resuts of comparatve estmaton of contro systems among three controers are gven. Tabe aso descrbes on-ne earnng and test resuts for dfferent amount of rues and dfferent number of teratons. Onne earnng resuts of contro systems wth three controers show that the ncreasng a number of rues from 6 to 48 decreases the vaue of sum of square errors. The test s carred out for 00 teratons. The 000 teraton- earnng resuts are used for test. Resuts of comparsons of RNFIS, NFIS and RNN based contro systems show that n the same condton the vaue sum of square of errors for RNFIS s ess than for others. Test resuts demonstrate the effcency of RNFIS for constructng controer. Exampe. The deveopment of contro system based on RNFIS s carred out for controng temperature of rectfer - coumn. Durng smuaton the mode of pant s descrbed by the foowng dfferenta equaton. dy dy(t) 0 + a + a y(t) = b u(t -τ ) dt dt a 0 (8) where a 0 = 0.056mn, a = 0.07mn, a =, o b 0 = 60 C/(kgf/cm ), τ = 5 sec, here y(t) s reguaton parameter of pant, u(t) s controer s output, τ s deay. Sampng tme for the pant s 5 sec. Computer smuaton of contro system wth RNFIS for pant (8) s carred out. The nta vaues of the parameters of membershp functons c and σ are chosen n the nterva [- 0, 0], c and σ n the nterva [ 0., 0.]. Number of rues are 6. Durng earnng the parameters of RNFIS are determned. Aso the deveopment of contro system wth NFIS and RNN for pant (8) s carred out. The earnng of controers based on RNFIS and NFIS are carred out at the same condton. The nta vaues of parameters for both networks are generated n the same nterva. In fgure 8 the curves that descrbe the test resuts of tme response characterstcs of contro systems wth RNN, NFIS and RNFIS are gven. The resuts of smuaton of contro system based on RNFIS show that the vaue of statc error of tme response characterstcs s absent (zero). Transent overshoot and settng tme of system wth RNFIS are ess than other types of controers. The resuts of smuaton and expermenta anayss of contro system wth RNFIS show that t has better tme response characterstc than others. Fgure 7. Test resut - tme response characterstc of contro systems based on RNFIS (sod ne), NFIS (dotted ne), and RNN (dashed ne). Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

9 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 TABE II RESUTS OF COMPARISON AMONG THREE CONTROERS Number of rues Number of teraton k = RNN NFIS RNFIS CPUtme k = CPUtme k = CPU - tme On ne earnng Test resuts Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/ Fgure 8. Test resut - tme response characterstc of contro systems based on RNFIS (sod ne), NFIS (dotted ne), and RNN (dashed ne). Smuaton resut of contro system based on RNFIS for pant (8) s compared wth the smuaton resuts of contro systems based on NFIS and RNN. In tabe 3 the resuts of comparatve estmaton of tme response characterstc of contro systems based on RNFIS, NFIS and RNN controers are gven. As shown n tabe III the vaue of sum of square errors for RNFIS based contro system s ess than others. The resuts of smuaton and expermenta anayss of the automatc contro system wth RNFIS show ts effcency. TABE III RESUTS OF COMPARISON Crtera RNN NFIS RNFIS CPU-tme M = Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764

10 Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Computer and Informaton Engneerng Vo, No7, 007 Internatona Scence Index, Computer and Informaton Engneerng Vo, No7, 007 waset.org/pubcaton/5764 IV. CONCUSION In ths paper the deveopment of recurrent neuro-fuzzy system for dentfcaton and contro of dynamc pant s consdered. The structure and earnng agorthms of RNFIS are descrbed. For earnng of network the supervsed agorthm s used. The earnng capabty of RNFIS aows automatcay construct tsef and to dea wth non-statonary pants. The smuaton resut of dentfcaton and contro systems based on RNFIS are compared wth other types of neura network based system. In dentfcaton probem the RNFIS test resuts have shown two tmes better performance n sum of square of errors than NFIS system. In contro RNFIS based contro system test resuts are compared wth RNN and NFIS based contro systems resuts and RNFIS based contro system has shown better performance than other types of systems. Resut of comparatve estmaton demonstrates the effcency of presented approach. REFERENCES [] Zadeh.A.(975). The concept of ngustc varabe and ts appcaton to approxmate reasonng. Informaton Scences, v.8. [] osko B. (993). Neura networks and fuzzy systems. A dynamca system approach to machne ntegence. Prentce- Ha Internatona Inc., Engewood Cffs. [3] Yager R.R., Zadeh.A.(Eds). (994). Fuzzy sets, neura networks and softcomputng, New York, Van Nostrand Renhod. [4] Wtod Pedryz, edtor, (996) Fuzzy Modeng Paradgms and Practce, uwer Academc Pubsher, Boston. [5] Aev R.A., Tserkovn A.E., and Mamedova G.A. (99). Producton management at fuzzy nta nformaton. Moscow, Energatomzdat, (Russan) [6] J.Reeman and D.Saad.(997). Onne earnng n rada bass functon networks, Neura Comput., vo.9,no.7, [7] T.Mheskes and B. appen. (993). Onne earnng processes n artfca neura networks. Math. Found. Neura Networks, Amsterdam, The Netherands Esever, pp [8] Dederch J. (990). Artfca Neura Networks. Consept earnng, os Aamtos CA IEEE Computer Socety Press. [9] Jyh-Shng Roger Jang. (993). ANFIS Adaptve-Network- Based Fuzzy Inference System. IEEE Transactons on Systems, Man and Cybernetcs, Vo.3, No.3, pp [0] Nauck, Detef and ruse, Rudof. (996). Desgnng neurofuzzy systems through backpropagaton, In Wtod Pedryz, edtor, Fuzzy Modeng Paradgms and Practce, Boston, uwer Academc Pubsher,pp.03-8 [] Detef Nauck. (994). Budng neura-fuzzy controers wth NEFCON-I. In Rudof ruse, Jorg Gebhardt, and Raner Pam(Eds), Fuzzy Systems n Computer Scence, Artfca Integence, Wesbaden, Veweg,pp.4-5. [] M.Onder Efe, and Okyay aynak. (000). On stabzaton of Gradent-Based Tranng Strateges for Computatonay Integent Systems. IEEE Transactons on Fuzzy Systems, Vo.8, No.5, October, pp [3] J.J.Buckey, Y.Hayash, and E.Czogoa.(993). Fuzzy neura networks wth fuzzy sgnas and weghts. Internatona Journa on Integent Systems 8, pp [4] J.J.Buckey, and Y.Hayash. (993). Fuzzy neura networks. In.A.Zadeh and R.R.Yager (Eds), Fuzzy Sets, Neura networks and Soft Computng, Van Nostrand Renhod, pp [5] H.Ishbuch,. Moroka, and H.Tanaka. (994). A fuzzy neura network wth trapezoda fuzzy weghts. Proc. FUZZ-IEEE, Orando, Forda, June 6-9, pp [6] R.A.Aev, R.H.Abyev, and R.R.Aev. (994). Automatc contro system synthess wth the earned neura network based fuzzy controer. Moscow, News of Academy of Scences, Tech. Cybernetcs pp [7] R.A.Aev, F.T.Aev, R.H.Abev, and R.R.Aev. (994). Industra neura controers. EUFIT 94, Promenade 9,5076, Aachen, Germany. Eta foundaton [8] R.H.Abyev,.W.Bonfg, and F.T.Aev. (996). Controer based on fuzzy neura network for contro of technoogca process. ICAFS-96, Segen, Germany, June 5-7,pp [9] J.Zhang, and A.J.Morrs, (999). Recurrent neuro-fuzzy networks for nonnear process modeng. IEEE Trans. Neura Networks, vo.0,no., Mart, pp.33-36, [0] C.H.ee, and C.C.Theng. (000). Identfcaton and contro of dynamc systems usng recurrent fuzzy neura network. IEEE Trans. Fuzzy Systems, vo. 8, pp [] Cha-Feng Juang. (00), A TS type recurrent fuzzy network for dynamc systems processng by neura network and genetc agorthm, IEEE Trans. Fuzzy Systems, vo.0, pp [] James eer, Ronad R.Yager, and Hossen Tahan. (99). Neura network mpementaton of fuzzy ogc, Fuzzy Sets and Systems, 45pp.-. [3] Rahb Abyev. (00). Controers based on Softcomputng eements// Eectrca, Eectroncs and Computer Engneerng Symposum NEU-CEE00 & Exhbton. Ncosa, TRNC, Turkey, May 3-5, pp [4] Rahb Abyev. (00). Fuzzy nference system based on neura network for technoogca processes contro. Journa of Mathematca and Computatona Appcatons. Turkey, pp [5] Jaer Nunez-Garca and Oaf Wokenhauer. (00). Random Set System Identfcaton. IEEE Transactons on Fuzzy Systems, Vo.0, No.3, October, pp [6] Rahb Abyev. (00). Neuro-Fuzzy system for technoogca processes contro. The 6 th Word Mut-Conference on SYSTEMICS, cybernetcs and nformatcs. SCI-000, Orando, Forda, USA. Juy 4-8. Rahb Hdayat Abyev was born n Azerbaan, n 966. He receved Ph.D degree n Eectrca and Eectronc Engneerng from Azerbaan State O Academy (od USSR). He worked research assstant at the research aboratory Industra nteectua contro systems of Computer-aded contro system department at O Academy for sx years. From 999-present he s workng as assocate professor at the department of Computer Engneerng of Near East Unversty, TRNC, Turkey. He s vce charman of Computer Engneerng Department. He has pubshed more than sxty papers n reated feds. He s member of IJCI, IJSP and IJIT from 003 and member of IEEE. Hs research nterests are Inteectua Contro Systems, Fuzzy Systems, Neura Networks, Genetc Agorthms, Chaos Theory, Sgna Processng, Pattern Recognton, Optmzaton. Internatona Schoary and Scentfc Research & Innovaton (7) schoar.waset.org/ /5764