鎽� 瑕侊細閲囩敤BP绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鍦ㄧ窔瑾�(di脿o)鏁碢ID鐨勪笁鍊嬪弮鏁�(sh霉)锛岄噰鐢℅RNN绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)浣滅偤杈ㄨ瓨鍣ㄥ湪绶氳鲸璀樻帶鍒惰几鍑哄皪鎺у埗杓稿叆灏嶈薄璁婂寲鐨勯潏鏁忓害淇℃伅锛屾彁楂樼郴绲�(t菕ng)鐨勬帶鍒剁簿搴︼紝閫�(j矛n)鑰岀法鍒禡ATLAB绋嬪簭閫�(j矛n)琛屼豢鐪�銆傝┎绠楁硶缍�(j墨ng)浠跨湡娓│锛岀祼(ji茅)鏋滆〃鏄庡叾鎺у埗鏁堟灉鑹ソ锛岄妫掓€у挤銆� 闂�(gu膩n)閸佃锛�BP绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌) GRNN绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌) PID 1 寮曡█ 銆€銆€鍦ㄥ伐妤�(y猫)鎺у埗涓�锛屽偝绲�(t菕ng)鐨凱ID鎺у埗鑷充粖浠嶈檿浜庝富灏�(d菐o)鍦颁綅锛屽挨鍏堕仼鐢ㄤ簬鑳藉缓绔嬫暩(sh霉)瀛�(xu茅)妯″瀷鐨勭⒑瀹氭€ф帶鍒剁郴绲�(t菕ng)銆傜劧鑰屽ぇ閲忕殑宸ユキ(y猫)閬庣▼寰€寰€鍏锋湁闈炵窔鎬�銆佹檪璁婁笉纰哄畾鎬х瓑鍥犵礌锛岄洠浠ュ缓绔嬪叾绮剧⒑鐨勬暩(sh霉)瀛�(xu茅)妯″瀷;鍙﹀锛孭ID 鎺у埗鍣ㄤ腑鐨勫弮鏁�(sh霉)閫氬父閮界敱浜哄伐鏁村畾锛岀敱浜庝竴娆℃€ф暣瀹氬緱鍒扮殑閫欎簺鍙冩暩(sh霉)寰堥洠淇濊瓑鍏舵帶鍒舵晥鏋滃绲傝檿浜庢渶浣崇媭鎱�(t脿i)鍥犳锛屽父瑕�(gu墨)PID 鎺у埗鍣ㄧ殑鎺у埗鏁堟灉鍜屾帶鍒剁簿搴﹀彈鍒颁簡闄愬埗. 绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鍏锋湁鑷(xu茅)缈�(x铆)銆佽嚜绲勭箶鍔熻兘鍜岃伅(li谩n)鎯宠鎲�銆佸苟琛岃檿鐞嗙瓑鍎�(y艒u)榛�锛屼娇鍏跺湪寰�(f霉)闆滅殑宸ユキ(y猫)鎺у埗涓緱鍒颁簡寤ｆ硾鎳�(y墨ng)鐢╗1,2]銆傜洰鍓嶆噳(y墨ng)鐢ㄨ純澶氱殑绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鏄熀浜嶣P 绠楁硶鐨勫灞ゅ墠楗嬬缍�(j墨ng)缍�(w菐ng)绲�(lu貌)锛岄€欑ó缍�(w菐ng)绲�(lu貌)鍙嶆槧鐨勬槸绯荤当(t菕ng)闈滄厠(t脿i)鐨勮几鍏�-杓稿嚭鏄犲皠闂�(gu膩n)绯�銆傛枃鐛�(xi脿n)[3]鎻愬嚭浜嗕竴绋熀浜庡皪瑙掑洖姝哥缍�(j墨ng)缍�(w菐ng)绲�(lu貌)锛坉iagonal recurrent neural network,DRNN锛夌殑鎺у埗绯荤当(t菕ng)銆傝垏闈滄厠(t脿i)缍�(w菐ng)绲�(lu貌)鐩告瘮锛岄€欑ó鍥炴缍�(w菐ng)绲�(lu貌)鍏锋湁杓冨ソ鐨勮檿鐞嗗嫊鎱�(t脿i)鍟忛鐨勮兘鍔�銆傜敱浜庡彧闇€杓冨皯鐨勭缍�(j墨ng)鍏冨拰娆�(qu谩n)鍊�锛屽洖姝哥恫(w菐ng)绲�(lu貌)鏇撮仼鍚堜簬铏曠悊鏅傝畩鐨勮几鍏ャ€佽几鍑洪亷绋媅4]銆� 鍩轰簬鍥炴绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勪笂杩扮壒榛烇紝鏈枃閲囩敤DRNN缍�(w菐ng)绲�(lu貌)锛岃ō(sh猫)瑷堝嚭姣斾緥銆佺⿳鍒嗐€佸井鍒嗙瓑鍙冩暩(sh霉)鍙互鍦ㄧ窔瀛�(xu茅)缈�(x铆)鐨凱ID鎺у埗鍣�锛屽苟灏囧叾鎳�(y墨ng)鐢ㄤ簬鏃ュ父鐢熸椿涓殑渚涚啽鎺у埗绯荤当(t菕ng)涓�锛岋紝寤虹珛浜嗕竴鍊嬪熀浜嶮ATLAB鐠�(hu谩n)澧冪殑鎺у埗浠跨湡銆� 2 鍩轰簬BP绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鎺у埗鐨凱ID绠楁硶 銆€銆€閲囩敤澶氬堡鍓嶅悜绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)-BP缍�(w菐ng)绲�(lu貌)灏峆ID鍙冩暩(sh霉)kp,ki,kd鍦ㄧ窔瑾�(di脿o)鏁�锛屽鍦�1鎵€绀�銆傜偤鍏呭垎鍙嶆噳(y墨ng)杓稿叆鎺у埗鍣ㄤ俊铏熺殑鐗规€э紝绲�(ji茅)鍚堟帶鍒跺櫒绲�(ji茅)妲�(g貌u)锛岄伕鎿囩恫(w菐ng)绲�(lu貌)杓稿叆灞ょ缍�(j墨ng)鍏冨€嬫暩(sh霉)鐐�4锛岃几鍑哄堡绁炵稉(j墨ng)鍏冨€嬫暩(sh霉)鐐�3.杓稿嚭灞ょ缍�(j墨ng)鍏冪殑娲诲寲鍑芥暩(sh霉)?銆傜锛坸锛�= 闅卞堡绁炵稉(j墨ng)鍏冩縺鐧�(f膩)鍑芥暩(sh霉)鍙栧嚱鏁�(sh霉)锛歠锛坸锛�=銆傜恫(w菐ng)绲�(lu貌)杓稿叆灞ょ殑杓稿叆鐐猴細O[sub]j[/sub]锛�1锛�=x锛坖锛�,1,2,3,4.缍�(w菐ng)绲�(lu貌)闅卞堡鐨勮几鍏ヨ几鍑虹偤net[sub]i[/sub]锛�2锛夛紙k锛�=,鈥�8.寮忎腑锛寃[sub]ij[/sub]锛�2锛夋槸闅卞惈灞ょ殑鍔犳瑠(qu谩n)绯绘暩(sh霉);闅卞惈灞ょ缍�(j墨ng)鍏冪殑娲诲寲鍑芥暩(sh霉)鍙杅锛坸锛�=銆傜恫(w菐ng)绲�(lu貌)杓稿嚭灞ょ殑杓稿叆杓稿嚭鐐猴細net[sub]l[/sub]锛�3锛夛紙k锛�= 寮忎腑锛寃[sub]li[/sub]锛�3锛夋槸杓稿嚭灞ゅ姞娆�(qu谩n)绯绘暩(sh霉)銆備笂杩板悇寮忎腑鐨勪笂妯�(bi膩o)锛�1锛�銆侊紙2锛�銆侊紙3锛夊垎鍒ヤ唬琛ㄨ几鍏ュ堡闅卞惈灞ゅ拰杓稿嚭灞�銆傝几鍑哄堡绁炵稉(j墨ng)鍏冪殑娲诲寲鍑芥暩(sh霉)鍙杇锛坸锛�=銆傛€ц兘鎸囨(bi膩o)鍑芥暩(sh霉)鐐篹锛坘锛�=1/2error[sup]2[/sup]锛坘锛�銆傛寜姊害涓嬮檷娉曚慨姝ｇ恫(w菐ng)绲�(lu貌)娆�(qu谩n)绯绘暩(sh霉)锛屽苟闄勫姞涓€鍊嬩娇鎼滅储蹇€熸敹鏂傚叏灞€妤靛皬鐨勬叄鎬ч爡锛�鐐哄(xu茅)缈�(x铆)閫熺巼;鐐烘叄鎬х郴鏁�(sh霉)銆傜敱浜�鏈煡锛屾墍浠ヨ繎浼肩敤绗﹁櫉鍑芥暩(sh霉)sgn锛�锛夊彇浠ｏ紝鐢辨甯朵締鐨勮▓绠椾笉绮剧⒑鐨勫奖闊垮彲浠ラ€氶亷瑾�(di脿o)鏁村(xu茅)缈�(x铆)閫熺巼 渚嗚鍎�銆� 銆€銆€鐢变笂闈㈢殑浠嬬垂鍙煡PID鐨勫閲忓紡鏂圭▼濡備笅銆倁 锛坘锛�=u锛坘-1锛�+kp锛坋锛坘锛�-e锛坘-1锛夛級+kie锛坘锛�+kd锛坋锛坘锛�-2e锛坘-1锛�+e锛坘-2锛夛級鐢辨鍙緱锛�?锛熷偦闀乄(w菐ng)绲�(lu貌)杓稿嚭灞ゆ瑠(qu谩n)鐨勫(xu茅)缈�(x铆)绠楁硶鐐猴細,l=1,2,3,4.鍚岀悊鍙緱闅卞惈灞ゅ姞娆�(qu谩n)绯绘暩(sh霉)鐨勫(xu茅)缈�(x铆)绠楁硶锛� , i=1,2,...,q. [align=center] 鍦�1 鎺у埗绯荤当(t菕ng)绲�(ji茅)妲�(g貌u)鍦朳/align] 3 DRNN杈ㄨ瓨缍�(w菐ng)绲�(lu貌) 銆€銆€DRNN绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鏄竴绋洖姝哥缍�(j墨ng)缍�(w菐ng)绲�(lu貌)銆傜恫(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)鍏变笁灞わ紝闅卞堡鐐哄洖姝稿堡锛屾墍浠ュ彲浠ュ皪鍕曟厠(t脿i)绯荤当(t菕ng)鏈夊緢濂界殑杈ㄨ瓨銆侱RNN绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勭祼(ji茅)妲�(g貌u)濡傚湒浜屾墍绀恒€� [align=center] 鍦�2 DRNN绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)鍦朳/align] 4 鍩轰簬DRNN杈ㄨ瓨鐨凚P绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)PID绠楁硶 銆€銆€鍩轰簬DRNN杈ㄨ瓨鐨凚P绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)PID鎺у埗绯荤当(t菕ng)鐨勭祼(ji茅)妲�(g貌u)濡傚湒3鎵€绀�銆傛帶鍒跺櫒鐢变笁鍊嬮儴鍒嗙祫鎴愶細锛�1锛夌稉(j墨ng)鍏窹ID鎺у埗鍣�锛岀洿鎺ュ皪琚帶灏嶈薄閬庣▼閫�(j矛n)琛岄枆鐠�(hu谩n)鎺у埗锛屽叾涓夊€嬪弮鏁�(sh霉)k[sub]p[/sub]锛宬[sub]i[/sub]锛宬[sub]d[/sub]鍦ㄧ窔鑷(xu茅)缈�(x铆)鏁村畾銆傦紙2锛塂RNN杈ㄨ瓨缍�(w菐ng)绲�(lu貌)锛岀敤浜庡缓绔嬭鎺у皪璞＄殑杈ㄨ瓨妯″瀷锛屼互渚垮嫊鎱�(t脿i)瑙€娓帶鍒跺皪璞＄殑杓稿嚭灏嶆帶鍒惰几鍏ョ殑闈堟晱搴�锛屾彁渚涚郸BP绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)銆傦紙3锛塀P绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)锛岄€氶亷瑾�(di脿o)鏁磋嚜韬瑠(qu谩n)绯绘暩(sh霉)锛屽皪PID鎺у埗鍙冩暩(sh霉)閫�(j矛n)琛岃(di脿o)绡€(ji茅)锛屼互閬�(d谩)鍒版煇绋€ц兘鎸囨(bi膩o)鐨勬渶鍎�(y艒u)銆� [align=center] 鍦�3 鎺у埗绯荤当(t菕ng)绲�(ji茅)妲�(g貌u)鍦朳/align] 銆€銆€鍩轰簬DRNN杈ㄨ瓨鐨凚P绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)PID鎺у埗绠楁硶濡備笅锛氾紙1锛夌⒑瀹欱P绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)锛屽苟绲﹀嚭鍊嬪堡娆�(qu谩n)绯绘暩(sh霉)鐨勫垵鍊紈[sub]ij[/sub]锛�2锛夛紙0锛夊拰w[sub]li[/sub]锛�3锛夛紙0锛夈€佸(xu茅)缈�(x铆)閫熺巼畏銆佹叄鎬х郴鏁�(sh霉)伪 ;k=1;锛�2锛塂RNN缍�(w菐ng)绲�(lu貌)杓稿叆灞ゃ€佸洖姝稿堡銆佽几鍑哄堡娆�(qu谩n)鍊艰肠浠ュ皬鐨勯毃姗熷€�锛屽苟瑷�(sh猫)瀹氱恫(w菐ng)绲�(lu貌)鍚勫堡鐨勫(xu茅)缈�(x铆)閫熺巼鍜屾叄鎬х郴鏁�(sh霉);锛�3锛夐噰妯ｅ緱鍒皔(t菕ng)锛坘锛夈€乺锛坘锛�锛岃▓绠梕锛坘锛�,鍚屾檪绲j锛坘锛夈€乹[sub]ij[/sub]锛坘锛夎肠闆跺垵鍊�;锛�4锛夋鍚戣▓绠桞P缍�(w菐ng)绲�(lu貌)鍚勫堡绁炵稉(j墨ng)鍏冪殑杓稿叆銆佽几鍑�;瑷堢畻PID鎺у埗鍣ㄧ殑杓稿嚭u锛屽苟閫佸叆鎺у埗灏嶈薄鍙奃RNN杈ㄨ瓨缍�(w菐ng)绲�(lu貌)锛岀敘(ch菐n)鐢熸帶鍒跺皪璞＄殑杓稿嚭yout锛坘锛�;锛�5锛夊皪DRNN缍�(w菐ng)绲�(lu貌)鐨勬瑠(qu谩n)鍊奸€�(j矛n)琛屽鏅備慨姝�锛岃鲸璀樿几鍑簓[sub]m[/sub]out锛坘锛�;锛�6锛夌敤BP缍�(w菐ng)绲�(lu貌)鐨勮凯浠ｇ畻娉曚慨姝P缍�(w菐ng)绲�(lu貌)娆�(qu谩n)绯绘暩(sh霉);锛�7锛変护k=k+1杩斿洖绗竴姝�锛岀辜绾�(x霉)鎸夋闋嗗簭鍩�(zh铆)琛�銆� 5 浠跨湡瀵︾従(xi脿n) 寮︽尝杓稿叆闊挎噳(y墨ng)鏇茬窔鍦栵紝寰炲湒涓彲浠ョ湅鍑哄叐姊濇洸绶氬熀鏈噸鍚�锛岃宸緢灏忋€傛ā鍨嬬殑璺熻工鑳藉姏姣旇純婊挎剰锛屽彲瑕�锛岀敱DRNN绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)妲�(g貌u)鎴愮殑杈ㄨ瓨缍�(w菐ng)绲�(lu貌)鏀舵杺閫熷害蹇紝绮惧害楂�銆� [align=center] 鍦�4 姝ｅ鸡璺熻工鏇茬窔[/align] 銆€銆€鐢变簬闆嗕腑渚涚啽閬庣▼涓�锛屼笉鍙伩鍏嶇殑瀛樺湪涓嶇⒑瀹氭€х殑鎿惧嫊閲�锛屽皪涓婅堪妯″瀷娣诲姞闅ㄦ鎿惧嫊閲忔脯瑭�锛屾脯瑭︽煇涓€鏅傚埢绯荤当(t菕ng)鍙楀埌涓€鍊嬪渚嗛毃姗熸摼鍕曠殑鑷仼鎳�(y墨ng)鎺у埗銆傚湒5-6鐐虹郴绲�(t菕ng)绐佸姞鎿惧嫊鏅傜殑浠跨湡鏇茬窔銆傜敱鍦栧彲浠ョ湅鍑�锛屽湪瀛樺湪鏌愪竴娈垫檪闁撶殑鎿惧嫊瑾ゅ樊閲忕殑鎯呮硜涓�锛屽熀浜嶥RNN杈ㄨ瓨鐨凚P绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)PID鎺у埗绠楁硶浠嶇劧椤ず浜嗗緢濂界殑鎺у埗鑳藉姏锛屾寮﹁窡韫ゆ洸绶氬熀鏈劇璁婂寲锛岄’绀轰簡灏嶇獊鐧�(f膩)鍕曟厠(t脿i)鎿惧嫊寰堝ソ寰堝挤鐨勬姂鍒惰兘鍔�銆� [align=center] 鍦�5 娣诲姞鎿惧嫊閲忕殑姝ｅ鸡璺熻工鏇茬窔 鍦�6 娣诲姞鎿惧嫊閲忕殑姝ｅ鸡璺熻工瑾ゅ樊鏇茬窔[/align] 6 鍓�(chu脿ng)鏂伴粸 銆€銆€閲囩敤浠P绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)浣滅偤鎺у埗鍣�锛屼互DRNN缍�(w菐ng)绲�(lu貌)浣滅偤杈ㄨ瓨鍣紝浣滅敤鍦≒ID鎺у埗鍣ㄤ笂锛岄嚌灏嶇郴鏁�(sh霉)鎱㈡檪璁娿€侀潪绶氭€уぇ涔嬪悗鐨�銆佸寘鍚摼鍕曠殑闆嗕腑渚涚啽鎻涚啽绔欐韩搴︽ā鍨嬮€�(j矛n)琛屾帶鍒讹紝浠跨湡绲�(ji茅)鏋滆〃鏄庯細铻嶅悎涓夌ó鎺у埗绛栫暐鐨勬绋帶鍒舵柟寮忔帶鍒舵晥鏋滆壇濂�銆侀妫掓€у挤銆� 鍙冭€冩枃鐛�(xi脿n) 銆€銆€閲戜互鎱э紝绋嬫帶鍒� .娓呰彲澶у(xu茅)鍑虹増绀�锛�1993锛�4 銆€銆€姣涙亽锛岀帇姘稿垵銆傜缍�(j墨ng)缍�(w菐ng)绲�(lu貌)鍦ㄩ亷绋嬫帶鍒朵腑鐨勬噳(y墨ng)鐢� .绂忓缓闆昏叇锛�2003锛岋紙9锛� 銆€銆€鍔夐噾鐞ㄣ€傚厛閫�(j矛n)PID鎺у埗鍙婂叾MALAB浠跨湡 銆傞浕瀛愬伐妤�(y猫)鍑虹増绀撅紝2003锛�1 銆€銆€瓒欓暦鍗狅紝涓嶅畬鍏ㄥ井鍒哖ID鎺у埗绠楁硶鐨勭爺绌惰垏鎳�(y墨ng)鐢�銆傝▓绠楁鑸囨暩(sh霉)瀛楀伐绋嬶紝2007锛�8 銆€銆€鍔夐噾鐞�锛屾櫤鑳芥帶鍒� 銆傞浕瀛愬伐妤�(y猫)鍑虹増绀撅紝2005锛�5 銆€銆€鍚宠(w猫i)鍏碉紝鍩轰簬RBF鍦ㄧ窔杈ㄨ瓨鐨勭缍�(j墨ng)缍�(w菐ng)绲�(lu貌)PID鎺у埗鍙婂叾鎳�(y墨ng)鐢�銆傚喍閲戣嚜鍕曞寲锛�2006锛�4 銆€銆€Rao J Rural.Neural nerwork architeure for parameter estimation of dynamical systems .IEEE Pror-CTA 1996,143锛�4锛�:387-393. 銆€銆€J J.H opfield,D.W.Tank.Neural Computation of Decisions Optimization Problen.Biological Cybernetics.1985,52:141-152