The PID Controller Based on the Artificial Neural Network and the Differential Evolution Algorithm

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1 2368 JOURNAL OF COMPUERS, VOL. 7, NO., OCOBER 22 he PID Controller Based on the Artfcal Neural Networ and the Dfferental Evoluton Algorthm We Lu he Control Scence and Engneerng Department of Dalan Unversty of echnology, Dalan, Chna Emal: Janhua Yang and Xaodong Lu he Control Scence and Engneerng Department of Dalan Unversty of echnology, Dalan, Chna Emal: Abstract he conventonal PID (proportonal-ntegraldervatve) controller s wdely appled to ndustral automaton and process control feld because ts structure s sample and ts robust s well, but t do not wor well for nonlnear system, tme-delayed lnear system and tmevaryng system. hs paper provdes a new style of PID controller that s based on artfcal neural networ and evolutonary algorthm accordng to the conventonal one s mathematcal formula. he artfcal neural networ (ANN) s used to approach PID formula and the dfferental evoluton algorthm (DEA) s used to search weght of the artfcal neural networ. hs new controller s proven better control effect n the smulaton test. hs new controller has more advantages than the conventonal one, such as less calculated load, faster global convergence speed, better robust, more ndependence and adaptablty on the plant and ndependent of human nterventon and expert experences etc. Index erms the artfcal neural networ, the dfferental evoluton algorthm, PID controller I. INRODUCION he conventonal PID (proportonal-ntegral-dervatve) controller s wdely appled to ndustral automaton and process control, for ts control mode s drect, smple and robust. But, there are some dsadvantages of PID control. Frstly, t s dffcult to regulate the three parameters of PID controller: K P, K I and K D n some control systems. Secondly, the conventonal PID controllers generally do not wor well for nonlnear system, tme-delayed lnear system, complex and vague system, tme varyng systems [][2][3][4]. Varous types of modfed PID controller have been developed, such as self-turnng PID controller, to overcome the one problem of the regulaton conventonal PID controller parameter. he fuzzy PID controllers and the neural networ PID controllers are also desgned for ths purpose. he natural representaton of control nowledge mae fuzzy controller easy to be understood [3]. But the most fuzzy controllers use two nputs, error, the change rate of error to approxmately behaves le a PD controller, and obvously there would exst steady-state error when ndustral process systems are controlled by fuzzy controller. It can elmnate the steady-state error of the control system to consder the ntegraton of error n nput of the fuzzy controller. Of course ths can be realzed by desgnng,a fuzzy controller wth three nputs, error, the change rate of error and ntegraton of error. However, t wll be hard to mplement n practce because of the dffculty n constructng control rules base. Frst, t s not the practce for expert to observe the ntegraton of error. Second, addng one nput varable n fuzzy controller wll greatly ncrease the number of control rules [7][8]. he artfcal neural networ has the ablty of learnng and functon approxmaton. In addton, the artfcal neural networ learnng processes are ndependent of human nterventon and expert experences. For such stuatons, many studes use ANN to approxmate PID formula to realze ANN-PID controller. But the learnng method of ANN usually adopts some tradtonal algorthm, ncludng the delta rule, the steepest descent methods, Boltzman s algorthm, the bac-propagaton learnng algorthm, the standard verson of genetc algorthm [9][][], etc. hese tradtonal learnng methods of ANN exsts some defcency ncludng such as the problem of the slow speed of convergence, local mnma, and the large amount of computaton of networ, etc, whch lead to ANN-PID controller s dffcult to use actually[5][6]. In ths paper, a new ANN PID controller whch s based on the dfferental evoluton algorthm (DEA) s proposed. Here, artfcal neural networ s used to approxmate PID formula and usng DEA to tran the weghts of ANN. he smulaton proves ths controller can get better control effect, and t s easly realzed and the less amount of computaton. he remander of the paper s organzed as fellows. Secton 2 brefly descrbed the conventonal ANN-PID controller. Secton 3 brefly ntroduced the basc dea of the dfferental evoluton algorthm. Secton 4 presents proposed the framewor and algorthm of the ANN-PID 22 ACADEMY PUBLISHER do:.434/jcp

2 JOURNAL OF COMPUERS, VOL. 7, NO., OCOBER controller based on the dfferental evoluton algorthm (ANN-PID-DEA). Secton 5 apples the proposed framewor and algorthm to fve examples wth dfferent complexty levels to demonstrate ts control ablty and learnng capablty of ANN-PID-DEA controller. Fnally, Secton 6 provdes the concluson. II. HE CONVENIONAL ANN-PID CONROLLER It s well nown, there are two tradtonal PID controller modes, one s locatonal mode, and the other s ncremental mode. he ANN realzaton of locatonal mode PID s shown below. It can be referenced to get the one of ncremental mode. ANN-PID controller generally adopts steepest descent method to learn weghts based on the objectve functon J. [ y ( + ) y( + ) ] J p (3) 2 Where, y p s the desred output of the controlled object at step +, y s the actual output of the controlled object at step +. As we all now, usng gradent descent method to tran u( K e( + e j j d ( + ( e( e( ) ) K Pe( + KIe j ( + K j D Δe( () where K p K, K I K/ I, K D K d, s the samplng perod, u( s output of the PID controller, e( s the devaton. For equaton (), u( s the lnear combnaton of e(, j e (, Δe j (,.e. Δe( u( f e(, e j (, (2) j Feed-forward ANN s used to construct an ANN-PID controller. Generally, a three layered feed-forward ANN wth approprate networ structure and weghts can approach to any random contnuous functon. he ANN s desgned wth three layers n consderaton of the control system real tme requrement. Obvously, there are three nodes n nput layer, the devaton e(, the cumulaton of devaton e j ( and the varety of devaton Δe(. Only one node n output layer, that s, the output of the controller u(. In order to smplfy the structure of the ANN, hdden layer nodes, whch can correctly reflect the relatonshp between the nput and the output of the ANN, are desgned as few as possble, and 8 nodes s assumed n ths paper. In practce, hdden layer nodes can be acqured by experment or experence [4][5][6]. he neuron actvaton functon of nput layer s assumed lnear functon f (x) x; that of hdden layer s assumed the Sgmod functon f h (x)/(+e -x ) and that of output layer s assumed lnear functon f o (x)x. So a 3-8- networ s constructed and s shown n Fg., whch can tae the place of tradtonal PID controller. In Fg., the ANN-PID three nputs of nput layer are e(, ANN-PID. j e (, Δe j (, u( s the output of Fgure ANN-PID controller. ANN leads to fallng nto local mnmum and slowng speed of converge, therefore n order to get rde of ths defect, n next secton, the dfferent evoluton algorthm (DEA) s adopted to tran weghts of the ANN-PID. III. HE DIFFERENIAL EVOLUION AL GORIHM he dfferent evoluton algorthm (DEA) s a branch of the evoluton algorthms, whch has been developed by Storn and Prce [7]. DEA s a smple evolutonary algorthm that creates new canddate solutons by combnng the parent ndvdual and several other ndvduals of the same populaton. A canddate replaces the parent only f t has better ftness. hs s a rather greedy selecton scheme that often outperforms tradtonal EAs. Le the other EA, utlzes N, n- dmensonal parameter weght vectors w,g,,..., N, as a populaton for each teraton, called generaton, of the DEA algorthm. he ntal populaton s taen to be unformly dstrbuted n the search space. At each teraton, the mutaton and crossover operators are appled on the ndvduals, and a new populaton arses. hen, the selecton phase starts, where the N best ponts from both populatons are selected to comprse the next generaton. Accordng to the mutaton operator, for each weght vector, w,g,,..., N, a mutant vector s determned through the equaton: ( W W ) V, G Wr, G + F r2, G r3, G + (4) where r, r2, r3 {,..., N}, are mutually dfferent random ndexes and also dfferent from the current ndex. F (, 2] s a real constant parameter that affects the dfferental varaton between two vectors, and N must be 22 ACADEMY PUBLISHER

3 237 JOURNAL OF COMPUERS, VOL. 7, NO., OCOBER 22 greater than or equal to 4, n order to apply mutaton. Followng the mutaton phase, the crossover operator s appled on the populaton, combnng the prevously mutated vector,v,g+ [v,g+,v 2,G+,,v D,G+ ] wth a socalled target vector, w,g+ [w,g+,w 2,G+,,w D,G+ ]. hus a so-called tral vector, u,g+ [u,g+,u 2,G+,, u D,G+ ] s generated, accordng to or u V, f (Randb(j) CR)orjrnbr() (5) j, G+ j, G+ u V, f (Randb(j)>CR) or j rnbr() (6) j, G+ j, G+ where l,..., N, randb(j) [, ] s the jth evaluaton of a unform random number generator, for j, 2,..., D, and rnbr(), 2,..., d s a randomly chosen ndex. CR [, ] s the crossover constant (user defned), a parameter that ncreases the dversty of the ndvduals n the populaton. he three algorthm parameters that steer the search of the algorthm are the populaton sze (N), the crossover constant (CR) and the dfferental varaton factor (m). hey reman constant durng an optmzaton. o decde whether or not the vector u,g+ should be a member of the populaton comprsng the next generaton, t s compared to the ntal vector w ;G. hus, ( u ) f ( w ) u, G +, f, G + <, G w, G + (7) w, G, otherwse he procedure descrbed above s consdered as the standard varant of the DE algorthm. Dfferent mutaton and crossover operators have been appled wth promsng results. In addton, DE algorthms have a property that Prce has called a unversal global mutaton mechansm or globally correlated mutaton mechansm, whch seems to be the man property responsble for the appealng performance of DE as global optmzers. o apply DEA algorthms to ANN tranng weghts as an ntal weght populaton, and evolve them over tme; N s fxed throughout the tranng process, and the weght populaton s ntalzed randomly followng a unform probablty dstrbuton. At each teraton, called generaton, new weght vectors are generated by the combnaton of the weght vectors randomly chosen from the populaton. hs operaton s called mutaton. he derved weght vectors are then mxed wth another predetermned weght vector, the target vector, through the crossover operaton. hs operaton yelds the so called tral vector. he tral vector s accepted for the next generaton f and only f t reduces the error value of the objectve functon J ((3)). hs last operaton s called selecton. he abovementoned operatons ntroduce dversty n the populaton and are used to help the algorthm escape the local mnma n the weght space. he combned acton of mutaton and crossover s responsble for much of the effectveness of DEA s search, and allows them to act as parallel, nose-tolerant, hll-clmbng algorthms, whch effcently search the whole weght space [22][23]. IV. HE ANN-PID LEARNING ALGORIHM BASED ON HE DEA As shown n the followng Fg. 2, ANN-DEA-PID s controller based on the artfcal networ and the dfferent evolve algorthm, r s system referenced nput, y s system output, u s controllng output of ANN-DEA-PID controller. Devaton e, cumulaton of devaton Σe and varety of devaton Δe are appled as the nputs of ANN- DEA-PID controller. In ths control system, we adopt the hybrd method combned of dfferental evoluton algorthm and steepest descent algorthm for ANN-DEA- PID. he DE algorthm wors on the termnaton pont of steepest descent algorthm. hus the method conssts of a steepest descent strategy-based ANN-DEA-PID tranng stage and a dfferental evolutonary strategy-based ANN- DEA-PID retranng stage. Fgure 2. he ANN-PID control system based on DEA.. A. Frst Stage: the Steepest Descent Algorthm for ANN- DEA-PID he proposed learnng procedure s based on the gradent descent learnng rule for ANNs learnng. In Fg., Input layer s weghts are,,. Input of hdden layer s jth neuron can be wrtten as follows: 3 I ω X (8) Where ω j s the weght whch connect jth(j,2 8) neuron n hdden layer wth th(,2,3) neuron n nput layer; X (,2,3) are the outputs of nput layer, that s: X e(, X 2 e j (, X 3 j Output of the jth neuron n hdden layer s: j Δe( (9) O f I ) () h ( Input of the neuron n output layer s 8 I ω O () o j ω j (j,2 8) s the weght whch connects the only neuron n output layer wth the jth neuron n hdden layer. Output of the neuron n output layer s j 22 ACADEMY PUBLISHER

4 JOURNAL OF COMPUERS, VOL. 7, NO., OCOBER O (2) o fo ( I o ) I o Output of the neutral networ PID controller s u (3) ( Oo f o ( I o ) I o ) Adjustng of Output Layer s Weghts Weght learnng rule s Δ ω j η (4) Where η s learnng speed, t commonly s (, ). j j + ) o y + ) ( o j ( y ( + ) y( + ) ) p O + ) u( (5) where + ) u( s unnown whch denotes system s nput-output relatonshp. For most systems, ts sgnal s defnte. + ) u( s replaced wth sgn( y( + ) u( ), and learnng speed η s used to equalze the calculate error. Adjustng rule of output layer s weghts ω j s: ω η + ) ω ( + j ( j + ) ( y ( + ) y( + ) ) O sgn( ) p j u( 2) Adjustng of Hdden Layer s Weghts Weght learnng rule s Δωj η j η η o o η O o X j ( O ) X 8 ω O η j o + ) ω j + ) o ( y ( + ) y( + ) ) p ω j X + ) ω j u( (6) (7) (8) wher + ) u( s replaced by sgn( y( + ) u( ), learnng speed η s used to equalze the calculate error. Correspondng adjustng rule of hdden layer s weghts ω j s: ω ( + ) ω ( j j ω O j ) + η( y p ( + ) y( + ) ) + ) ( O ) X sgn( ) u( (9) A generc descrpton of the proposed hybrd algorthm s gven n Algorthm. Algorthm. Stage : the steepest descent learnng Step a: Decde networ structure at frst. Because the nodes of networ nput layers and output layers are nown, only the nodes of hdden layers remaned undecded. Step 2a: Intalze the weghts of hdden layers ω j and the ones of output layers ω j wth less random number, select the speed of learnng η; Step 3a: Repeat for each nput concept state (. Step 4a: Sample the system, get e(, j Δe( e j (,, whch are the networ nputs; Step 5a: Accordng to formula (9) and () calculate the outputs of hdden layer and output layer, get the controllng amount u; Step 6a: Calculate the system output and get y( +) ; Step 7a: Accordng to the weghts adaptng rule (5) and (8) of output layer and hdden layer, regulate each connecton weght of output layer and hdden layer. Step 8a: Calculate objectve functon J Step 9a: Untl the termnaton condtons are met. Stepa: Return the fnal weghts W SDA (+) to the Stage 2. Stage 2: the dfferental evoluton learnng Step 2b: Intalze the DE populaton n the neghborhood (+) of W SDA and wthn the suggested weght constrants (ranges). Step 2b: Repeat for each nput concept state (. Step 3b: For to NP. ( Step 4b: MUAION (w ) Mutant_Vector. Step 5b: CROSSOVER (Mutant_Vector) ral_vector. ( Step 6b: If J (ral_vector) J(w ), accept ral_vector for the next generaton. Step 7b: End For. Step 8b: Untl the termnaton condton s met. Frst, the steepest descent algorthm s outlned n the Stage of Algorthm, and provdes convergence of concepts values n a desred state. he ey features of the steepest descent algorthm method are the low storage requrements and the nexpensve computatons. In Stage 2 of Algorthm, the dfferental evoluton (DE) algorthm, responsble for the ANN-DEA-PID retranng s outlned. B. Second Stage: the Dfferental Evoluton Algorthm o apply DEA algorthms to ANN-PID retranng weghts startng wth a specfc number (N) of n- 22 ACADEMY PUBLISHER

5 2372 JOURNAL OF COMPUERS, VOL. 7, NO., OCOBER 22 dmensonal weght vectors, as ntal populaton, and evolve them over tme; N s fxed throughout the tranng process, and the weght populaton s ntalzed by perturbng the approprate soluton provded by the steepest descent algorthm. Also, the approprate ftness functon s determned. In ths case, the steepest descent algorthm seeds the DE,.e. a prelmnary soluton s avalable by the steepest descent algorthm; so, the ntal populaton mght be generated by addng normally dstrbuted random devatons to the nomnal soluton. However, n the experments reported n the next secton, we have also used the constrants on weghts defned ntally by experts to perturb the approxmated soluton provded by steepest descent algorthm. Let us now gve some detals about the verson of DE algorthm used here. Steps 4b and 5b mplement the mutaton and crossover operators, respectvely, whle Step 6b s the selecton operator. For each weght vector w ( the new vector called mutant vector s generated accordng to the followng relaton: Mutant vector v ( + ) ( ( ( ( w w + w w ), w + μ best r r2 (2),2L NP ( Where w best s the best populaton member of the prevous teraton, μ> s a real parameter (mutaton constant) whch regulates the contrbuton of the dfference between weght vectors, and w r, w r2 are weght vectors randomly chosen from the populaton wth r, r2 {l, 2,..., -l, +,..., N},.e. r, r2 are random ntegers mutually dfferent from the runnng ndex. Amng at decreasng the dversty of the weght vectors further, the crossover-type operaton yelds the so-called tral vector, u (+),,..., N. hs operaton wors as follows: the mutant weght vectors (v (+),,..., N) are mxed wth the target vectors, w (+), l,..., N. Specfcally, we randomly choose a real number r n the nterval [, ] for each component j, j, 2,..., n, of the (+) v. hs number s compared wth CR [, ](crossover constant), and f r CR; then, the jth component of the tral vector u (+), gets the value of the (+) jth component of the mutant vector v ;otherwse, t gets the value of the jth component of the target vector, w (+). he tral vector s accepted for the next generaton f and only f t reduces the value of the followng (+) proposed ftness functon J; otherwse the old value, w s retaned. hs last operaton s the selecton, and due to the movng optmum nature of the dfferental evoluton tas, t ensures that the ftness J starts steadly decreasng at some teraton. Here, clearly, the ftness functon J s formula (3). he purpose s to determne the values of the weghts of the ANN-DEA-PID that produce a desred behavor of the system. he determnaton of the weghts s of major sgnfcance and t contrbutes towards the establshment of ANN-DEA-PID as a robust methodology, and mproves the performance of ANN-DEA-PID. V. SIMULAION ANALYSIS he neural networ PID controller wth the dfferental evolutonal algorthm, whch s proposed n ths paper, s a constructed by neural networ PID controller and the dfferental evolutonal algorthm. In ths new PID controller, the artfcal neural networ s used to approach the conventonal PID formula and the dfferental evoluton algorthm (DEA) s used to search weght of the artfcal neural networ. Fve examples wth dfferent complexty levels are descrbed n ths secton and are used for the smulatons. A. Frst Order System he frst example s the frst order systems model as follow G ( s) (2) 95s + For ths delay tme system, the parameters are chosen as follow: sample perod s s, reference value r, the tradtonal PID controller parameters are K p 23,K.375,K d.2. he output response obtaned s shown n Fg. 3 as curve for step nput sgnal. Curve 2 n Fg.3 shows the result of ANN-DEA-PID controller wth the 3-8- neural networ and ANN s learnng speed s.. Curve 3 n Fg.3 also depcts the output performance of the ANN-PID controller wth the 3-8- neural networ n whch the parameters after learnng are: s, s, r,and ANN s learnng speed s.. Fgure 3. he ANN-PID control system based on DEA. B. Frst Order System wth me Delay he second example s the frst order systems wth the tme dealy model as follow s e G( s) 95s + (22) 22 ACADEMY PUBLISHER

6 JOURNAL OF COMPUERS, VOL. 7, NO., OCOBER For ths delay tme system, the parameters are chosen as follow: sample perod s s, reference value r, the tradtonal PID controller parameters are K p 3,K.325,K d.8. he output response obtaned s shown n Fg. 4 as curve for step nput sgnal. Curve 2 n Fg.4 shows the result of ANN-DEA-PID controller wth the 3-8- neural networ and ANN s learnng speed s.. Curve 3 n Fg.4 also depcts the output performance of the ANN-PID controller wth the 3-8- neural networ n whch the parameters after learnng are: s, s, r,and ANN s learnng speed s.. For ths process, the sutable parameters of conventonal PID controller are consdered as: sample perod s.5s, reference value r ; K p.92, K.279, K d he curve of output response that mared curve s shown n Fg 6. For ANN-PID controller wth the 3-8- neural networ and ANN s learnng speed s., the output response, called curve 2, s gven n the same tme. Curve 3 n Fg.6 gves the result of ANN-DEA-PID controller wth the 3-8- neural networ and ANN s learnng speed η.. Fgure 5. he control effect of PID, ANN-PID and ANN-DEA-PID controller for second order system. C. Second Order System he second example s the second order systems wth the smple model as follow G ( s) (23) s( s + ) For ths second order system, the parameters are chosen as follow: sample perod s.5s, reference value r8, the tradtonal PID controller parameters are K p 3.57,K.25,K d.2. he output response obtaned s shown n Fg. 5 as curve for step nput sgnal. Curve 2 n Fg. 5 shows the result of ANN-DEA-PID controller wth the 3-8- neural networ and ANN s learnng speed s.. Curve 3 n Fg. 5 also depcts the output performance of the ANN-PID controller wth the 3-8- neural networ n whch the parameters after learnng are: s, s, r,and ANN s learnng speed s.. D. Second Order System wth me Delay he thrd example s the second order system wth tme delay. he model of t s obtaned as followng G( s) e 2s ( s + )( 23s + ) (24) Fgure 6. he control effect of PID, ANN-PID and ANN-DEA-PID controller for frst order system wth tme delay. Fgure 4. he control effect of PID, ANN-PID and ANN-DEA-PID controller for second order system wth tme delay. E. the me Varable Nonlnear System Durng the smulaton, a typcal tme varable nonlnear system, whch model s a ( y( ) + u( ) y (, 2 + y ( ) 22 ACADEMY PUBLISHER

7 2374 JOURNAL OF COMPUERS, VOL. 7, NO., OCOBER 22 π a ( +.sn (25) 25 It s taen as the controlled object. Obvously, the conventonal PID controller can not be appled to tme varable nonlnear system such as (24). In here, he ANN-DEA-PID controller wth the 3-8- neural networ structure and the tradtonal ANN-PID controller are appled respectvely. When the nput sgnal s square wave wth ampltude s [-,] and perod s s.he control system sample perod s s.5s, the correspondng response curves are shown n Fg.6 and Fg.7. From Fg.7 and Fg.8, t s obvous that the control effect of ANN-DEA-PID controller better than ANN-PID controller and the ANN-DEA-PID controller s more ndependent and adaptable on the model of the controlled object. hs also exactly reflects the outstandng learnng and retanng ablty and self-adaptng ablty of neural networ. In addton, the dfferent evolve algorthm s adopted to tran weghts of networ, whch promotes the performance of the control system and decrease calculated load. Fgure 7. he control effect of ANN-PID controller for the tme varable nonlnear system. Fgure 8. he control effect of ANN-DEA-PID controller for the tme varable nonlnear system. VI. CONCLUSION he advantages of the ANN-PID controller based DEA are summarzed as followng:. he mathematcs model for the controlled object s not necessary; 2. he structure of the controller and the algorthm s smple, and t s convenent to apply them to onlne realtme control; 3. It s more robust. he method can be appled to ndustral process control, and tae full advantage of both neural networ and tradtonal PID. 4. ANN-PID controller based on DEA convergence speed s faster than ANN-PID controller and ANN-DEA- PID controller can reach global mnmum, due to adopt the dfferent evolutonal algorthm to tran weght of neural networ. REFERENCES [] Yu Yongquan, Huang Yng and Zeng B, A PID Neural Networ Controller, Proceedng of the Internatonal Jont Conference on Neural NetWors, IEEE Copmuter Socety Press,Calforna, vol. 3, pp , 23. [2] Yue Pan,Png Song and Keje L, PID Control of Mnature Unmanned Helcopter Yaw System based on RBF Neural Networ, Intellgent computng and Informaton Scence,vol. 35,pp ,2. [3] Haquan Wang, Dongyun Wang and Guotao Zhang, Research of Neural networ PID Control of Aeroengne, Advances Automaton and Robotcs, vol., pp , 2. [4] Iwasa,.,Morzum,N.andOrmatu,S. emperature Control n a Batch Process by Neural Networs, Proceedng of IEEE World Congress on Computatonal Intellgence, IEEE Press,New Yor, vol. 2, pp , 992. [5] L q, L shhua. Analyss and Improvement of a Knd of neural Networs Intellgent PID Control Alogrthm, Control and Decson Edtoral Department, ShenYang Chna, vol. 3, pp. 3-36, 998. [6] Morad,M.H. New echnques for PID Controller Desgn, Proceedng of 23 IEEE Conference on Control Applcatons, IEEE Press,New Yor, vol. 2, pp , 23. [7] Indranl Pan,Saptarsh Das,Amtava Gupta, unng of an optmal fuzzy PID controller wth stochastc algorthms for networed control systems wth random tme delay, ISA ransacton, vol. 5, pp , 2. [8] G.jahed, M.M.Ardehal, Genetc algorthm-based fuzzy- PID control methodologes for enhancement of energy effcency of a dynamc energy system, Energy Converson and management, vol. 52, pp ,2. [9]. Bac,H.P. Schwefel. An overvewof evolutonary algorthms for parameter optmzaton, Evol. Comput., pp. 23,993. [] N. Dodd, Optmzaton of networ structure usng genetc technques, n Proceedngs of the 99 Internatonal Jont Conference on Neural Networs, 99. [] P. Bartlett,. Downs, ranng a Neural Networ Usng a Genetc Algorthm, ech. Report, Department of Electrcal Engneerng, Unversty of Queensland, 99. [2] H.G. Beyer, H.P. Schwefel, Evoluton strateges: a comprehensve ntroducton, Nat. Comput., vol., pp. 3 52, 22. [3] Saptarsh Das,Indranl Pan,Shantanu Das,etc, A novel fractonal order fuzzy PID controller and ts optmal tme doman tunng based on ntegral performance ndces, Engneerng Applcatons of Artfcal Intellgence, onlne,2. [4] I.L. Lopez Cruz, L.G. Van Wllgenburg, G. Van Straten, Effcent dfferental evoluton algorthms for multmodal optmal control problems, Applcaton Soft Computng,vol. 3, pp ,23. [5] G.D. Magoulas, V.P. Plagannaos, M.N. Vrahats, Neural networ-based colonoscopc dagnoss usng onlne learnng and dfferental evoluton, Appl. Soft Comput., vol. 4, pp , 24. [6] Mohannad Anwar Hosen,Mohd Azlan Hussan,Farouq S.Mjall, Control of polystyrene batch reactors usng 22 ACADEMY PUBLISHER

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