【正文】 Eq.(8) into Eq.(1) and Eq.(2), the following equation canbe derived: )()1( thty ??? （ 10） )]1(,),1(),(),(),1(,),([:)( ?????? uy ntututrtKntytyt ??? （ 11） where ny _ 3, nu _ 2, and h() denotes a nonlinear function. Since the future output y(t + 1) included in Eq.(13) cannot be obtained at t, y(t+1) is replaced by r(t+1). Because the control system so that can realize y(t + 1) ! r(t + 1), is designed in this paper. Therefore, 175。 Nichols method[2] or Chien, Hrones amp。 = K(N(0)) in the initial stage. [STEP 2] Calculate distance and select neighbors Distances between the query )(tl? and the informationvectors ))(( kii ?? are calculated using the following L1norm with some weights: ? ?? ? ??? 11 )(m i n)(m a x )()()))((),(( uy nn l ll mm jtjtd ?? ???? （ 16） where N(t) denotes the number of information vectors storedin the database when the query )(t? is given. Furthermore, )(jl? denotes the lth element of the jth information , )(tl? denotes the lth element of the query at t. Moreover, )(max ml? denotes the maximum element among the lth element of all information vectors ))(,2,1),(( tNjj ??? stored in the database. Similarly, )(min ml? denotes the minimum element. Here, k pieces with the smallest distances are chosen from all information vectors. [STEP 3] Construct local model Next, using k neighbors selected in STEP 2, the localmodel is constructed based on the following LinearlyWeighted Average(LWA)[12]: ??? ki id iKwtK 1 )()(? （ 17） where wi denotes the weight corresponding to the ith information vector )(i? in the selected neighbors, and is calculated by: ? ??? ???? 11 22 ))](m i n)([m a x )]()([1(nynu l ll ll mm itwi ?? ?? （ 18） [STEP 4] Data adjustment In the case where information corresponding to the current state of the controlled object is not effectively saved in the database, a suitable set of PID parameters cannot be effectively calculated. That is, it is necessary to adjust PID parameters so that the control error decreases. Therefore, PID parameters obtained in STEP 3 are updated corresponding to the control error, and these new PID parameters are stored in the database. The following steepest descent method is utilized in order to modify PID parameters: )( )1()()( tKtJtKtK dne w ? ???? ?? （ 19） ],[: DIP ???? ? （ 20） where _ denotes the learning rate, and 饎 he following J(t+1)denotes the error criterion: 2)1(21:)1( ??? ttJ ? （ 21） ).()(:)( tytyt r ??? （ 22） yr(t) denotes the output of the reference model which isgiven by: )()( )1()( 11 trzT Tzty r ??? (23) .1:)( 22111 ??? ??? ztztzT (24) Here, T (z?1) is designed based on the reference literature[13]. Moreover, each partial differential of Eq.(19) is developed as follows: . ????????????????????????????????????????????????????????????????????????????????????????????)()1())2()1(2)()(1()()()()1()1()1()1()1()()1()()1()()1()()()()1()1()1()1()1()()1()()1())1()()(1()()()()1()1()1()1()1()()1(tutytytytyttKtututytytttJtKtJtutytettKtututytytttJtKtJtutytytyttKtututytytttJtKtJDDIIPP????????? （ 25） Note that a priori information with respect to the systemJacobian )( )1( tuty? ?? is required in order to calculateEq.(25). Here, using the relation x = |x|sign(x), the systemJacobian can be obtained by the following equation: ),)( )1(()( )1()( )1( tutys igntutytuty ? ??? ???? ?? （ 26） where sign(x) = 1(x 0), ?1(x 0). Now, if the sign of the system Jacobian is known in advance, by including )()1( tuty ??? in ? , the usage of the system Jacobian can make easy[14]. Therefore, it is assumed that the sign of the system Jacobian is known in this paper. [STEP 5] Remove redundant data In implementing to real systems, the newly proposed scheme has a constraint that the calculation from STEP 2 to STEP 4 must be finished within the sampling time. Here,storing the redundant data in the database needs excessive putational time. Therefore, an algorithm to avoid the excessive increase of the stored data, is further discussed. The procedure is carried out in the following two steps. First, the information vectors )(i? which satisfy the following first condition, are extracted from the database: [First condition] ktNiitd ??? )(,2,1,))(),(( 1 ???? （ 27） wherei )(i? s defined by ?,2,1)],()([:)( ??? iiKii ? （ 28） Moreover, the information vectors )(i? which satisfy the following second condition, are further chosen from the extracted )?(i? : 2231 )()()( ???????????? ???l n e wln e wlltK tKiK （ 29） where )?(i? is defined by ?,2,1?)].?(),?([:)?( ??? iiKii ? （ 30） If there exist plural )?(i? , the information vector with the smallest value in the second condition among all, )?(i? is only removed. By the above procedure, the redundant datacan be removed from the database. Here, a block diagram summarized mentioned above algorithms are shown in Fig.