Iterative Learning Control with a Forgetting Factor for Consensus Tracking in Multi-Agent Systems
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- Πηνελόπεια Λύκος
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1 33 E-mal: :... : Ierave Learg Corol wh a Forgeg Facor for Cosesus racg Mul-Age Sysems Jgy Zheg Xogxog He Ymg Wu Zhehua Q College of Iformao Egeerg Zhejag Uversy of echology Hagzhou 33 Cha E-mal: hxx@zju.edu.c Absrac: Recely erave learg corol (ILC has bee used he feld of he mul-age sysems. I hs paper we frs propose a model for he leader-followg mul-age sysem cosesus racg problem from he perspecve of ILC. ILC s used o esure ha all followg ages perfecly rac he oly leader s rajecory a fe me erval as he erave umber goes o fy. he he forgeg facor s roduced o ILC o deal wh he al sae shf. A suffce codo s proposed o guaraee he forgeg facor ILC cosesus racg acheveme. Fally a smulao example s gve o show he effecveess of he forgeg facor ILC. Key Words: Mul-Age Sysem Cosesus racg Ierave Learg Corol Ial Shf Problem Forgeg Facor. (Iroduco [-5]. UAV.. (leader. - leader-follower [6-8].. [9] []. [-] [ ]. 9 Ah [9]. Lu [3]. Yag [4] /6/$3. c 6 IEEE 6859
2 . ILC.. Meg [5] τ. Yag [6] D. [7] PD.. Yag [8] DPD. Meg [9] LMI. - [] G = ( V E AG V E A G. v V = ej = v vj v v j v j v. v v j (pare. AG = a j aj > v vj E aj = v vj E j. a = =. v = { j: vj v E} v. Δ = j v a j= Δ= dag( Δ Δ Δ Laplaca L=Δ A G. v v j p: v v v vm vs vj v pah v j. spag ree (roo. E G ( V E A. = G. m R R R m. A A. I ( ( roecer. x= [ x x x ] R x x = = x x = x x x x. = max = m A= a j R A A = A A A = max m a j j. ρ( A A. f ( sup = f( = max [ ] f( f( = max [ ] e f(. f( f( e f(. 3.. G = ( V E AG. d v v. v d > d = h Chese Corol ad Decso Coferece (CCDC
3 G = ( V v E AG E = E v v AG = d AG D= dag( d d d. d = ( d d d : G = ( V E. G = ( V E. x ( = f( x( + Bu( y( = Cx( ( s x R ( u R ( m y R. x ( = f ( x( + Bu(. y( = Cx( : f( x ( Lpschz f( x( f( x( b x( x (. f 3: CB. 4: IIC Idecal Ial Codo x ( = x (. y ( = = y y ( = y ( [ ] =. 3. y (. yj ( v j. 4 ξ ( = a ( y ( y ( + d ( y ( y ( j j j e( = y ( y(. 5 (4(5 ξ( = [ ξ ( ξ ( ξ ( ] E ( = [ e ( e ( e (] (4(5.6 ξ ( = a ( e( e ( + d e ( j j j (6 ξ ( = ( L Im E ( + ( D Im E(. 7 = [( L+ D I ] E( u+ ( = ( α u ( + αu ( +Γξ ( 8 m Γ R < u (. m U( = [ u ( u ( u (] X( = [ x ( x ( x (] Y( = [ y ( y ( y (] Φ= dag[ α α α ] Γ= dag[ Γ Γ Γ ] ( X ( = F( x( + ( I B U( 9 Y( = ( I C X( F( x( = dag ( f ( x( f ( x (. U ( = [ u ( u ( u ( ] (8 U+ ( = [( I Φ I] U( + [ Φ I] U( +Γ [( L+ D I ] E ( 4. : 8-4 Φ Γ ( I [( ( I B ρ ( Φ I Γ L+ D Im] C < u u y y. α. : + u ( u+ ( = ( α( u ( u ( + α ( u ( u ( Γ ξ ( m α (5 u( U+ ( = [( I Φ I]( u( U ( + [ Φ I]( u( U( Γ [( L+ D Im] E ( Δ U ( = u ( U (. (3 6 8h Chese Corol ad Decso Coferece (CCDC 686
4 . Γ=Γ [( L+ D Im = [( I Φ + I] + [ Φ I] Γ [( L+ D Im] E = [( I Φ I] + [ Φ I] Γ E E = y Y = ( Cf ( x + CBu { ( I C[ f ( X + ( I B U]} = ( Cf ( x + CBu [( I C f ( X + (4 ( I CB U] = ( I C[( f( x f( X ] + ( I CB[ u U] (3(4 Δ U+ = [( I Φ I Γ ( I CB ] +Φ [ I ]. (5 Γ ( I C[( f( x f( X ] + ( I Φ I Γ ( I CB +Φ I. + Γ { I C f( x f( X } 6 ρ Κ = ( I Φ I Γ ( I CB (6 ρ +Φ I = b bb. Γ c f + Κ { c f } + bγ b x X ρκ +Φ I + x X x X. x X x X ( f( x + B( u dτ f( x f( X x ( X ( + dτ B u U + x X + b ( x f( X dτ ( ( + ( f( X + BU f ( ( bb u U + f f ( τ ( ( B ( x X e + e b u U (7 dτ 8 (7(8 ρ + b + Κ ρ + b Δ U + ΔX ( e f ( τ f x ( X ( e + f ( τ + e ( b ( ( B u τ U τ dτ Κ + b e ( τ dτ B Φ Φ f (9 = max( f e e ρ e + b e + Κ Φ + ΔX ( e ( f ( τ bb e e U ( τ d + Δ ( ρ + b + Κ Φ ( + Δ X ( + ( e ( = ρκ + ( e + b Δ U + ΔX ( Φ τ ( ( ( ρ = ρκ + ( e ρ + b + ΔX ( + ( Φ M ( M bφ + Δ X ( + ρ Δ U + M (3 ρ Κ < ρ <. lm U Δ ρ M (4 lm U u + M ρ. Δ X = x X ΔX ( f ( τ Δ X ( + e dτ ( f Δ X ( + ( e. f ( h Chese Corol ad Decso Coferece (CCDC
5 Δ Y Δ Y = y Y ( I C( x X (6 ( I C ΔX Δ X ( = α = + ρ lm Δ U lm Δ Y y( = [] Φ= dag( α α α3 α4 α5 (8 = dag( [4] Γ= ( CB ( L+ D + 5( L+ D.3. Γ =Γ = Γ3 = Γ4 = Γ 5 = (9.4. [ u ( u ( u ( u ( u ( ] = [ x( x( x3( x4( x5( ] = (( I Φ I Γ [( L+ D I ]( I CB ρ m m =.54 (. - Laplaca A G = L = D= dag( d d d d d = dag( x ( x ( + x ( u ( = + x ( cos( x ( 4 3 u ( (7 x ( y ( = x ( = 3 45 Ζ x( = x( = x3( = x4( = x5( = h Chese Corol ad Decso Coferece (CCDC 6863
6 [] Jadbabae A L J Morse A S. Coordao of groups of moble auoomous ages usg eares eghbor rules[j]. Auomac Corol IEEE rasacos o 3 48(6: [] Olfa-Saber R Murray R M. Cosesus problems ewors of ages wh swchg opology ad me-delays[j]. Auomac Corol IEEE rasacos o 4 49(9: [3] Re W Beard R W. Cosesus seeg mulage sysems uder dyamcally chagg eraco opologes[j]. IEEE rasacos o auomac corol 5 5(5: [4] Cheg L Hou Z G a M e al. eural-ewor-based adapve leader-followg corol for mul-age sysems wh uceraes[j]. eural ewors IEEE rasacos o (8: [5] Cao Y Yu W Re W e al. A overvew of rece progress he sudy of dsrbued mul-age coordao[j]. Idusral Iformacs IEEE rasacos o 3 9(: [6] Hog Y Hu J Gao L. racg corol for mul-age cosesus wh a acve leader ad varable opology[j]. Auomaca 6 4(7: [7] Re W. Mul-vehcle cosesus wh a me-varyg referece sae[j]. Sysems & Corol Leers 7 56(7: [8] Wag Y Cheg L Re W e al. Coame corol of mul-age sysems wh dyamc leaders based o a PI-ype approach[j] IEEE rasacos o Cyberecs press DOI:.9/CYB [9] Ah H S Che Y Q. Ierave learg corol for mul-age formao[c]//iccas-sice 9. IEEE 9: [] Meg D Ja Y. Ierave learg approaches o desg fe-me cosesus proocols for mul-age sysems[j]. Sysems & Corol Leers 6(: [] Moore K L Che Y Q Ah H S. Ierave learg corol: A uoral ad bg pcure vew[c]//proceedgs of he 45h IEEE Coferece o Decso ad Corol. 6: [] Xu J X. A survey o erave learg corol for olear sysems[j]. Ieraoal Joural of Corol 84(7: [3] Lu Y Ja Y. A erave learg approach o formao corol of mul-age sysems[j]. Sysems & Corol Leers 6(: [4] Yag S Xu J X Huag D e al. Opmal erave learg corol desg for mul-age sysems cosesus racg[j]. Sysems & Corol Leers 4 69: [5] Meg D Ja Y Du J e al. racg corol over a fe erval for mul-age sysems wh a me-varyg referece rajecory[j]. Sysems & Corol Leers 6(7: [6] Yag S Xu J X Huag D. Ierave learg corol for mul-age sysems cosesus racg[c]//decso ad Corol (CDC IEEE 5s Aual Coferece o. IEEE : [7]. [D]. 4. [8] Yag S Xu J X Re Q. Mul-age cosesus racg wh al sae error by erave learg corol[c]//corol & Auomao (ICCA h IEEE Ieraoal Coferece o. IEEE 4: [9] Meg D Ja Y Du J. Robus Cosesus racg Corol for Mulage Sysems Wh Ial Sae Shfs Dsurbaces ad Swchg opologes[j]. eural ewors ad Learg Sysems IEEE rasacos o 5 6(4: [] Hezger G Fewc D Pade B e al. Robus leag corol[c]//decso ad Corol 989. Proceedgs of he 8h IEEE Coferece o. IEEE 989: [] Olfa-Saber R Murray R M. Cosesus problems ewors of ages wh swchg opology ad me-delays[j]. Auomac Corol IEEE rasacos o 4 49(9: h Chese Corol ad Decso Coferece (CCDC
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