SOFT COMPUTING OPTIMIZER FOR INTELLIGENT CONTROL SYSTEMS DESIGN: THE STRUCTURE AND APPLICATIONS

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1 SOFT COMPUTING OPTIMIZER FOR INTELLIGENT CONTROL SYSTEMS DESIGN: THE STRUCTURE AND APPLICATIONS Sergey A. PANFILOV, Ludmla V. LITVINTSEVA, Ilya S. ULYANOV, Kazuk TAKAHASHI, Sergue V. ULYANOV YAMAHA Motor Euroe N.V. R&D Offce, Va Bramante, 65, 26013, Crema (CR), Italy Alexander V. YAZENIN Det. of Informatcs, Tver State Unversty, Ul. Zhelyabova 33, , Tver, Russan Federaton and Takahde HAGIWARA YAMAHA-Motor Co., LTD, 2500 Shnga, Iwata, Shzuoka, , Jaan Abstract. Soft Comutng Otmzer (SCO) as a new software tool for desgn of robust ntellgent control systems s descrbed. It s based on the hybrd methodology of soft comutng and stochastc smulaton. It uses as an nut the measured or smulated data about the modeled system. SCO s used to desgn an otmal fuzzy nference system, whch aroxmates a random behavor of control obect wth the certan accuracy. The task of the fuzzy nference system constructon s reduced to the subtasks such as formng of the lngustc varables for each nut and outut varable, creaton of rule data base, otmzaton of rule data base and refnement of the arameters of the membersh functons. Each task by the corresondng genetc algorthm (wth an arorate ftness functon) s solved. The result of SCO alcaton s the desgn of Knowledge Base of a Fuzzy Controller, whch contans the value nformaton about develoed fuzzy nference system. Such value nformaton can be downloaded nto the actual fuzzy controller to erform onlne fuzzy control. Smulatons results of robust fuzzy control of nonlnear dynamc systems and exermental results of alcaton on automotve sem-actve susenson control are demonstrated. Keywords: Soft comutng otmzer, knowledge base, ntellgent control, robust fuzzy controller, ftness functon 1. INTRODUCTION Fuzzy control has emerged as one of the most actve and frutful felds n ractcal alcaton of fuzzy systems theory based on a fuzzy logc and fuzzy sets theory ntroduced by L. Zadeh (1973). From control desgn ont of vew, fuzzy systems became so attractve because they can be consdered as unversal aroxmator of systems wth unknown dynamcs and structure. Fuzzy controllers (FC) allow for a smler, more human aroach to control desgn and rovde reasonable, effectve alternatve to classcal controllers (for examle, see [1]). Fuzzy systems are based on a logc aroach, whch enables us to translate qualtatve knowledge about the roblem nto a reasonng system caable of erformng aroxmate attern matchng and nterolaton. But, n fuzzy logc based technology the generaton of membersh functons (MF) and fuzzy rules (FR) s a task manly done by a human exert. Human exert also solves the task of refnng (or tunng) of knowledge base. It means that fuzzy logc aroach tself does not have adataton and learnng caabltes for self-constructng and tunng of MF's, and FR's. Fuzzy control system can be desgned by usng soft comutng technology ncludng Genetc Algorthms (GA) and Fuzzy Neural Networks (FNN) learnng algorthms [1]. Man dsadvantage of FNN-based aroaches s that the FNN structure must be gven a ror (.e., the number and tye of MF must be ntroduced by a user), but some tmes t s dffcult to defne otmal FNN structure manually. To avod ths dsadvantage, we develoed SCO as the new flexble tool for desgn of otmal structure and otmal knowledge base of a fuzzy system (for examle, a FC) based on some measured or smulated data ( teachng atterns ) about the modeled system. Random traectores of the chaotc behavor of control obect are generated by the stochastc smulaton wth arorate robablty densty functon accordng to the soluton of Fokker- Planck-Kolmogorov equatons. And wth fuzzy smulaton we study the ndvdual eculartes n the random dynamc behavor of control obect through the defnton of ftness functon. Desgn of KB for robust fuzzy controller s based on the extracton of the value nformaton about random dynamc behavor of control obect usng ftness functon n stochastc and fuzzy smulaton technologes. We demonstrate SCO tool s effcency and robustness for desgn of new tyes of selforganzng ntellgent control systems adated to control of essentally nonlnear stable and unstable lants under dfferent knds of stochastc exctatons. 2. INFORMATION-THERMODYNAMIC BOUNDS IN DESIGN PROCESS OF INTELLIGENT CONTROL SYSTEMS Fgure 1 shows the structure of self-organzng ntellgent control system based on SCO whch aroxmates measured or smulated data about the modeled system wth desred accuracy (call t as a teachng sgnal -TS). SCO uses chan of GAs to solve otmzaton roblems connected wth the otmal choce of number of MFs, ther shaes and arameters and wth otmal choce of fuzzy rules. Informaton-thermodynamc aroach to desgn of ftness functons n GAs s based on the analyss of dynamc behavor of control obect and FC [2]. Prncle of mnmum of entroy roducton n control obect and fuzzy PIDcontrollers s the background for desgn of ntellgent robust control. Robustness of control means that the mnmum of ntal nformaton about uncertanty of external envronments or structure s dsturbances of control obect s requred. Robustness crteron backgrounds. The roblem of maxmum of released work,.e. max( W ), where q, u are generalzed qu, SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 1 - NUMBER 5 91

2 coordnate and control corresondngly, s equvalent to the assocated roblem of the mnmum of entroy roducton,.e. mn( S ) [2,3]. For the general class of dynamc control systems, q, u descrbed by Hamlton-Jacob-Bellman equatons, the otmal soluton of the varatonal fxed-end roblem for the maxmum work W s equvalent to the soluton of varatonal fxed-end roblem for the mnmum entroy roducton [3]. Thus, the analytcal formalsm, whch s strongly analogous to those n analytcal mechancs and control theory, s effectve n thermodynamc otmzaton too. Let us consder the dynamc control rocess descrbed as follows: q = ϕ( q, t, u). Accordng to generalzed thermodynamc aroach [2,4], we can choose 1 n Lyaunov functon V for ths rocess as V = q + S, 2= 1 2 where S s entroy roducton of an oen system descrbed by q. S = S Sc, where S s the entroy roducton of a lant (control obect) and S c s the entroy roducton of controller (fuzzy PID-controller). Fgure 1: Structure of self-organzng robust ntellgent control system based on SCO Fgure 2: Flow chart of SC Otmzer After smle transformatons (as n [2]) we have dv n ds dsc = q ϕ( q, t, u) + ( S Sc) dt = 1 dt dt. (1) The nterrelaton between Lyaunov stablty (V) and robustness ( mn( S S ) ) descrbed by Eq.(1) s the general hyscal law for desgn of ntellgent control systems [2,4,5]. We aly ths law for desgn of smart KB of robust ntellgent control systems based on SCO tools. Thus, SCO s the unversal aroxmator, whch extracts nformaton from smulated (or measured) data about the modeled system. SCO guarantees the robustness of FC,.e. successful control erformance n wde range of lant s arameters, reference sgnals, and external dsturbances. Informaton bounds consdered n [2] are descrbed n Table THE STRUCTURE OF SOFT COMPUTING OPTIMIZER Fgure 2 shows the flow chart of SCO oeratons on macro level and combnes several stages. Table 1: Tyes and the role of GA ftness functon n SCO Tye of GA Crtera Ftness Functon HX = X log( ) X = ( x x = µ ) log X ( x x = µ X ) = MAX of mutual nformaton 1 N entroy µ X ( x ( ))log ( ( )) max t µ X x t GA_1: N t= 1 AND ( l, ) H X l X = H k x x= µ X, xk= µ = X Lngustc k Varables MIN 1 N l Otmzaton = µ X ( x ( )) ( ( )) of nformaton t µ X x k k t N t= 1 amount l n each sgnal log µ X ( x ()) ( ()) mn t µ X x k k t where * denotes selected T-norm (Fuzzy AND) oeraton. GA_2: MIN of total error E = E mn (a dfference between, Rule Base the FIS and TS where Otmzaton oututs) 2 E = 1/ 2( d F( x1, x2,..., x n )) MIN of total error E = E mn (a dfference between GA_3: FIS and TS oututs) OR Refne KB MAX of mutual nformaton entroy H X max The Role of FF Data comressng; Choce of otmal number of MF aroxmatng TS Choce of otmal number of rules and MF arameters Fne Tunng of MF arameters Stage 1: Fuzzy Inference System (FIS) Selecton. The user makes the selecton of fuzzy nference model wth the featurng of the followng ntal arameters: Number of nut and outut varables; Tye of fuzzy nference model (Mamdan, Sugeno, Tsukamoto, etc.); Prelmnary tye of MFs. Stage 2: Create lngustc values. GA otmzes lngustc varable arameters, usng the nformaton obtaned on Stage 1, and TS, obtaned from the n-out tables, or from dynamc resonse of control obect (real or smulated n Matlab). Stage 3: Rule base otmzaton. GA otmzes a rule base, usng the fuzzy model obtaned on Stage 1, otmal lngustc varable arameters, obtaned on Stage 2, and the same teachng sgnal as t was used on Stage 1. Stage 4: Refne KB. On ths stage, the structure of FNN s already secfed and close to global otmum. In order to reach the otmal structure, two methods can be used. Frst method s based on the mnmum error crtera and smlar to classcal dervatve based otmzaton rocedures (lke error back roagaton algorthm for FNN tunng), wth combnaton of ntal condtons for back roagaton, obtaned on revous otmzaton stages. Second method s based on the maxmum of mutual nformaton entroy crtera. The result of the Stage 4 s a secfcaton of fuzzy nference structure, otmal for soluton of a current roblem. In order to have robust soluton, Stage 4 can be byassed, and the robust structure obtaned wth GAs of stages 2-3 can be used. 92 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 1 - NUMBER 5

3 4. MAIN SCO-OPERATIONS SCO uses GA aroach to solve otmzaton roblems connected wth the otmal choce of number of MFs, ther shaes and arameters and wth otmal choce of fuzzy rules. GA's are known as a very comutatonal exensve aroach n otmzaton, snce each chromosome created durng genetc oeratons must be evaluated. For examle, GA wth oulaton sze of 100 chromosomes evolved 100 generatons requres as a maxmum calculatons of the ftness functon. Usually ths number s smaller, snce t s ossble to add some routne whch wll trace the same chromosomes, and wll not evolve them two tmes, but stll the total number of calculatons s much greater than number of evaluatons requred by some sohstcated classcal otmzaton algorthm. Ths comutatonal exense s a ayback for the robustness of FC obtaned when GA s used. The great number of the evaluatons gves the constrants on the ractcal alcatons of the GA. For examle, f the evaluaton functon requres 10 mnutes for calculaton on the sngle rocessor, ts evaluaton wth abovementoned GA wll take 10*10000 mnutes, whch s about 1600 hours, and ths tme grows exonentally wth ncreasng of the comlexty of the ftness functon. Ths ractcal constrant on GA alcaton, leads to develong of the smler ftness functons, dvdng the total goal of the algorthm (KB extracton of the chosen FIS) nto several smler roblems. Therefore SCO uses chan of GAs to solve otmzaton roblems connected wth the followng subroblems: (1) Defne number and shae of MFs; (2) Select otmal rules; (3) Fx otmal rules structure; and (4) Refne the KB structure. Informaton-thermodynamc crtera from [2] as ftness functons of GAs n SCO are used and guarantee the robustness of ntellgent control. In Table 1 tyes and the role of SCO-GA s ftness functons (FF) are shown. fnal form of the ftness functon of control n ths case s as follows: dsp dsc f = ( S SC) dt dt ; (3) ds dsθ dsl ds 2 = + ; c = kd e dt dt dt dt TS for the gven control roblem was obtaned n [6]. The SCO alcaton result of ntellgent fuzzy control of the swng system s resented n Fgure 3 n comarson wth classcal PID control and wth fuzzy control, where KB was obtaned by usng FNN error back-roagaton method [6]. Ftness functons n GAs of SCO are chosen from Table 1. Coeffcent gans of fuzzy PIDcontroller obtaned wth resented aroach have more stable behavor comarng wth coeffcent gans obtaned wth FNN based aroach (see Fgure 4). Fgure 3: Result of ntellgent control of swng system (controlled state varable) 5. SCO-APPLICATIONS EXAMPLES We comare the results of robust fuzzy control obtaned wth resented aroach and wth other soft comutng based aroaches. Consder unstable control obect as a swng dynamc system. The nonlnear equatons of moton of the swng dynamc system are: l g θ + 2 θ + snθ = 0 l l 2 1 l + 2kl l θ gcos θ = k e + k e + k e dt + ξ( t) m ( l d l l ) (2) Here ξ () t s the gven stochastc exctaton wth an arorate robablty densty functon. Equatons of entroy roducton are ds l the followng: θ ds = 2 θ θ; l = 2kl l. The system, dt l dt descrbed by Eq.(2), reresents a globally unstable (along a generalzed coordnate l) dynamc system. Examle: Fuzzy Control of swng system wth one PIDcontroller. We study a control roblem only for the second state varable of the swng system (the length l ). As a ftness functon ndcatng the better control, we choose the mnmum of the entroy roducton rate n the control obect (lant) and mnmum of the entroy roducton rate n the control system [2,4]. The Fgure 4: Behavor of the coeffcent gans of fuzzy PIDcontroller Examle: Fuzzy Control of swng system wth two PIDcontrollers. Consder excted moton of the swng system under fuzzy control of two PID-controllers along θ and l-axes usng the followng condtons. Let the system be dsturbed by two dfferent noses actng along θ and l-axes. Exctaton along θ - axs s descrbed by a Gaussan-lke nose and exctaton along l- SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 1 - NUMBER 5 93

4 axs s descrbed by a Raylegh-lke nose. Stochastc smulaton of random exctatons wth arorate robablty densty functons based on non-lnear formng flters methodology n [7] s develoed. The followng swng arameters and ntal condtons are consdered: m = 1, k = 1 and [ θ 0 = 0.25, l 0 = 1.5] [ θ 0 = 0, l 0 = 0.01]. The reference sgnals are as follows: θ = 0.4; l = 3.5. Tradtonal FNN based aroxmaton of TS. At ths ste we extract KB of FC by usng suervsed learnng of FNN wth error back roagaton algorthm. For realzaton of ths ste we use AFM tools develoed by STM [17]. FNN based KB desgn rocess s descrbed as follows: Numbers of MFs for each nut varables have to be chosen manually: 3; Number of rules n KB: 3x3x3x3= 81 rules. Remark: For the gven case, f we choose more than 3 MFs for each nut varables, AFM error back roagaton algorthm s faled. SC Otmzer based aroxmaton of TS. FC KB desgn rocess by SC Otmzer s characterzed as follows: Otmal numbers (and ther shaes) of MFs for each nut varables s defned by GA 2 : 9; Comlete number of fuzzy rules: 9x9x9x9 = 2331 rules; Otmal KB s defned by GA 2 : 143 rules. Control qualty and robustness comarson. Comare control qualty and robustness roerty of FC SCO obtaned by SCO, FC FNN obtaned by tradtonal SC aroach based on FNNtunng and classcal PID Controller. Results of comarson are shown n Fgure 5. Let us take FC SCO and FC FNN develoed for the case above (see Fgure 5) and use them n a new control stuaton. Let us consder the followng new ntal condtons [ ( 30 ), 2.5] [0.01, 0] (reference sgnals and noses are the same as n Fgure 5) and comare control erformance of FC SCO (obtaned by SCO), FC FNN obtaned by tradtonal SCaroach based on FNN-tunng, and tradtonal PID Controllers wth K = (8 6 8) for control along theta-axs and K = (7 6 7) for control along length-axs (see Fgure 6). Remark. We take these K-gans as mean values of varable K- gans obtaned by SCO. Smulaton results show that and FC SCO control s robust, FC FNN control s not robust when ntal condtons are changed. Fgure 7 shows the comarson of ftness functon values whch are estmated by Eq.(3) (generalzed entroy characterstcs of control) n the new control stuaton (see Fgure 6). From the smulaton results n Fgures 6 and 7 we can see that fuzzy PID-controller desgned by SCO realzes effectve control n comarson to FNN and tradtonal PID-controller where K- gans have been chosen by hel of SCO. But SCO Controller s more effectve than tradtonal PID Controller because t roduces much smaller entroy than PID Controller (see Fgure 8). Consder another control condtons (control stuaton 2): (1) ntal condtons [-0.52 ( 30 ), 2.5] [0.01, 0]; (2) new reference 0 sgnals:θ = 0.78 ( 45 ); l = 5; (3) new noses amltudes: nose along θ s a Gaussan-lke nose wth max amltude A = 1.5; and nose along length l s a Raylegh-lke nose wth max amltude A = 1.5. Fgure 5: Comarson of control qualty obtaned by SCO, FNN and tradtonal l PID controller Fgure 6: Control qualty comarson of FC SCO, FC FNN and tradtonal PID controller n the new control stuaton. Fgure 7: Ftness Functon amount comarson of FC SCO, FC FNN and tradtonal PID controller n a new control stuaton In ths case max amltudes of noses are 2 and 6 tmes smaller than n the case of KB desgn wth the TS n Fgure 5. Comare 94 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 1 - NUMBER 5

5 control erformance of FC SCO (obtaned by SCO) and FC FNN (obtaned by tradtonal SC-aroach based on FNN-tunng) (see Fgure 9). methodology of a fuzzy controller for a sem-actve susenson system usng genetc algorthms that otmzes only the membersh functons [9] was begun orgnally by Karr. Hashyama et al. exanded the functon of genetc algorthms to fnd control rules [10][11], and the algorthms they develoed were based on skyhook control of Karno [12] wth some orgnal addtons. Hagwara et al. [13] resented an dea for a method to create a knowledge base that s comletely self-organzed accordng to only ftness functons wthout any other redefned rule base [13], and an dea for an effectve knowledge base creaton method [6]. In ths reort we exand an dea by alyng SC otmzer for KB desgn and refnement. In order to make t ossble to reresent non-lnear movement, four local coordnates for each susenson and three for the vehcle body, totalng 19 local coordnates are consdered to form a mathematcal vehcle model (see Fgure 11). Equatons of moton are derved by Lagrange s aroach [13][14]. Fgure 8: Plant and controller entroy roducton under FC SCO, FC FNN and tradtonal PID controller n new control stuaton Smulaton results show that FC SCO control s robust, and FC FNN control s faled (unstable),.e. t s not robust when ntal condtons and reference sgnals are changed and dsturbance amltudes are much smaller. Fgure 10 shows the comarson of ftness functon values whch are estmated by Eq.(3) (generalzed entroy characterstcs of control) n the control stuaton 2. The smulaton results n Fgures 9 and 10 show that fuzzy PID-controller desgned by SCO realzes effectve control n comarson to FNN and tradtonal PIDcontroller. FC SCO and a tradtonal PID controller n control stuaton 2 Fgure 10: Ftness Functon comarson of Otmzaton of ntellgent control of shock absorber based on soft comutng technology (FNN aroach) s develoed n [14], [15] and [16]. Prncal arameters of the test vehcle are resented n [13]. As a ftness functon for SCO n ths examle we choose the mnmum of the low frequency (less than 2Hz) comonents of heave, tch and of roll movements of the car body. Exermental results resented n the Fgure 12 demonstrate better reducton of the selected low frequency comonents of the vehcle movements under actual control condtons when susenson system s controlled by fuzzy controller reared by SCO Fgure 9: Control qualty comarson of FC SCO, FC FNN and a tradtonal PID controller n control stuaton 2 Examle: Intellgent control of sem-actve automotve susenson system. We have aled ths tool also to desgn ntellgent control systems n ractcal areas such as ntellgent control of sem-actve vehcle susenson system. Persectve nterrelatons between SCO and quantum comutng technologes of robust controller desgn are consdered n [8]. Desgn Fgure 11: Mathematcal vehcle model SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 1 - NUMBER 5 95

6 Fgure 12: Exermental results of fuzzy control of sem-actve susenson system 6. CONCLUSIONS Wth SCO tool, usng a GA-based randomzed search of otmal robust control, we have modeled dfferent versons of robust KB s of FC, whch allow us to control essentally non-lnear stable and, esecally, unstable dynamc systems n the resence of uncertanty nformaton about external exctatons and n the resence of changng reference sgnals. The robustness of control laws s acheved by the ntroducton of vector GA-ftness functons, one of whch contans hyscal rncle of mnmum entroy roducton rate as n a control obect and n a control system. Such aroach allows us: (1) to desgn otmal ntellgent control system wth maxmal level of relablty and controllablty for comlex dynamc systems n the resence of uncertanty n ntal nformaton [4]; (2) to decrease the number of sensors as n a control crcut channel and n a measurng system wthout loss of accuracy and qualty of control [5]. The robust ntellgent control system desgned on the bass of such aroach needs the mnmum of ntal nformaton as about the behavor of controlled obect and about external random exctatons. Exermental results of effectve fuzzy ntellgent control of automotve sem-actve susenson system based on SCO alcaton are demonstrated. SCO tools are the background of a new hgh nformatonal desgn technology of smart robust control systems. 7. REFERENCES [1] L.V. Ltvntseva and S.V. Ulyanov, Artfcal Intellgence aled to desgn of ntellgent systems (a Soft Comutng Aroach), Lectures Notes, Vol.38, Note del Polo (Rcerca), Unversta degl Stud d Mlano, 2000, 134. [2] S.V.Ulyanov, K.Yamafu, V.S.Ulyanov, S.A. Panflov, et al., Comutatonal ntellgence for robust control algorthms of comlex dynamc systems wth mnmum entroy roducton. Part1: Smulaton of entroy-lke dynamc behavor and Lyaunov stablty, J. of Advanced Comutatonal Intellgence, 1999, Vol.3, No.2, ; B.N. Petrov, G.M. Ulanov and S.V. Ulyanov, Models of control rocesses: Informatonthermodynamcs aroach, Moscow, Sc. Publ, 1978; Informaton-semantc roblems n control and organzaton systems, bd, [3] S. Senutycz, Hamlton-Jacob-Bellman theory of dssatve thermal avalablty, Phys. Rev., 1997, Vol. 56E, No 5, [4] US Patent N 6,411,944 B1, 1997, Self-organzng control system (Inventor: S.V.Ulyanov) [5] USPatent N 6,415,272 B1, 1998, System for ntellgent control based on soft comutng (Inventor: S.V. Ulyanov) [6] S.A.Panflov, L.V. Ltvntseva, S.V. Ulyanov, K.Takahash and A.V.Yazenn, The stochastc smulaton system of robust fuzzy control of essentally non-lnear dynamc systems based on soft comutng, Proc. ICAFS 2002, Mlan, Italy, Setember 17-18, 2002, [7] S.V. Ulyanov, M. Feng, K. Yamafu, I. Kurawak et all, Stochastc analyss of tme-varant nonlnear systems. Pts 1,2, Intern. J. Probablstc Engneerng Mechancs, Vol. 13, No 3, 1998, [8] S.V. Ulyanov, K. Takahash, S.A. Panflov, L.V. Ltvntseva, I.S. Ulyanov, I. Kurawak, T. Hagwara and A.V. Yazenn, Desgn of robust ntellgent control systems based on soft and quantum comutng: From 1965 wth our teacher B.N. Petrov, In: Proc. Conference on Control System Desgn (Dedcated to the memory of B.N. Petrov), Moscow, 11 March, 2003, Sc. Publ., 2003, [9] C.L.Karr, Desgn of an Adatve Fuzzy Logc Controller Usng a Genetc Algorthm, Proc. of the 4th. Int l Conf. on Genetc Algorthms, 1992,. 450/457. [10] T. Hashyama, T. Furuhash, Y. Uchkawa, Fuzzy Controllers for Sem-Actve Susenson System Generated through Genetc Algorthms, Proc. of IEEE Int l Conf. Syst Man Cybern,, Vol.95, No. 5, 1995,. 4361/4366. [11] T. Hashyama, T. Furuhash, and Y. Uchkawa, On Fndng Fuzzy Rules and Selectng Inut Varables for Sem-Actve Susenson Control Usng Genetc Algorthm, Proc. of 11th Fuzzy System Symosum, 1995, [12] D. Karno, et al., Vbraton Control Usng Sem-Actve Force Generators, ASME J. of Engneerng for Industry, Vol.96, No.2, 1974, [13] T. Hagwara, S.A. Panflov, S.V. Ulyanov, K. Takahash and O. Damante, Alcaton of smart control susenson system based on soft comutng to a assenger car, Yamaha Motor Techncal Revew , No.35. [14] US Patent N 6,212,466, 2000, Otmzaton control method for shock absorber (Inventors: S.V. Ulyanov, T. Hagwara) [15] US Patent N 6,496,761, 2000, Otmzaton control method for shock absorber (Inventors: S.V. Ulyanov, T. Hagwara) [16] US Patent N 6,463,371, 1998, System for ntellgent control of the vehcle susenson based on soft comutng (Inventors: S.V. Ulyanov, T. Hagwara) [17] Adatve Fuzzy Modeler (AFM), htt://eu.st.com 96 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 1 - NUMBER 5