Linearized kappa guidance

Abstract

A b s t met 2. Dynamical EquationsThe 6-guidance dynamical equations, which are nonlinear and vary with respect to the independent parameter, range, are linearized and then the LQR method is used to solve the optimal control problem.The linearization is via a nonlinear coordinate transformation and nonlinear feedback. The cost function is approximated by a quadratic cost.

Lead Angle Constrained Optimal Midcourse Guidance

“…The further development of the this guidance law led to another approach, kappa-guidance that exploits the curvature and torsion along the intercept trajectory parameterized along the arc length or range to the predicted impact point. 29 All these paper has solve the optimal problem for a given terminal condition, however choice of terminal condition optimally is still a gray area.…”

Midcourse guidance law with neural networks

“…In an optimal setting, the resulting trajectory seeks to maximize the pursuer velocity at the time of intercept. Two types of guidance law have been popular in the midcourse guidance literature; they are the explicit guidance [1] and the optimal curvature or kappa guidance [2][3][4][5]. A linearized form of kappa guidance is proposed by Serakos and Lin [5] in which a coordinate transformation is used.…”

“…Two types of guidance law have been popular in the midcourse guidance literature; they are the explicit guidance [1] and the optimal curvature or kappa guidance [2][3][4][5]. A linearized form of kappa guidance is proposed by Serakos and Lin [5] in which a coordinate transformation is used. All of these guidance law are optimality based and use some sort of approximations to the non-linear equations of motion.…”

تعمیم راهکار هدایت کاپا به منظور بهبود مسیر بازگشت به محل معین یک سامانه ی هوایی با قید کمترین سرعت فرود

“…}=Q[ =@ =B=m C}=Oy uwv=k \UwD xOW|L= Q] |xv=t=U |}=yv CaQU Q=Okt u}vJty w ?=DW C= Q}}eD u= R}t w O@=} Ow@y@ |O=yvW}B T=U= Q@ xU}=kt w |@=} RQ= =@ "OwW xOv=UQ pk=OL x@ |Owta |xLiY QO |R=wQB CQwYx@ xv=t=U Q@ OQ=w ?=DW |xJN}Q=D xm OwW|t xOy=Wt 'xOt;CUOx@ G}=Dv "CU= xDi=} Ow@y@ |UwULt =B=m C}=Oy uwv=k |iQat "2 Q=OQ@ "Ov=|}=yv CaQU w |}x_Lr CaQU Q=OQ@ u}@t ? }DQDx@ v1 w v |=yQ=OQ@ u; hqDN= |x}w= R "OyO|t u=Wv = Q OYkt =D |}x_Lr |@Uv |xrY=i Q=OQ@ R}v R u=mt pY=w Q=OQ@ x@ C@Uv CtU |x}w= R u}vJty ' t f w t u}@ CaQU |x}w= R "CU= OYkt w |}x_Lr [25] "xOvwWC}=Oy |xv=t=U |Oa@ xU R=wQB C=YNWt KQ] "1 pmW pL 'Q=my= Q u}= QO "CU= 1 xv}y@ pQDvm |o}=Uty |D}=Oy OQ@y= Q R= xO=iDU= xQ=@ |o}=Uty QO Q=my= Q u}= "O};|t CUOx@ `HQt Q}Ut l} pwL 'xv}y@ |xDU@ |xkrL =t= &CU= xO=O x=Q= = Q |QDy@ ?=wH 2 u}mD C=W=WDe= Q=my= Q x@ C@Uv `HQt Q}Ut Q}}eD = Q OwN Q}Ut CU= umtt xm |}=wy h=Oy= |= Q@ u}vJty w x}rw= \}=QW Q}}eD =@ |xv}tR QO xDiQ}PBCQwY |=yQ=m w =yVqD xrtH R= "OwW|t pmWt Q=JO OvyO "OQm xQ=W= [8] Q=twm w [7] [9] "OwW xO=iDU= 3 Q}Ut OvDUy |Y=N |=y|oS}w |= Q=O xm |QPo \=kv CtU x@ C}=Oy xmr@ 'OwW|tv hOy l} CtU x@ xv=t=U ' [9] |WywSB QO , qFt "OvyO|t pmW = Q |@U=vt Q}Ut x@ w OwW|t C}=Oy 'O}t=v lQLDt QPo |x]kv l} = Q u; u=wD|t xm 4 xOvRer |R=Ht u}vJty "OwW|t pY=L xv=t=U |v=}t R=i C}=Oy |= Q@ ?U=vt |Q}Ut j} Q] u}= '|L]UQ}R |xv=t=U l} pQDvm w C}=Oy |xrUt |UQQ@ x@ [10] Qo}O |WywSB QO xOW xDN=OQB 'lQLDt QPo |x]kv C}=Oy uwv=k R= xO=iDU= =@ C@=F hOy ZQi =@ "CU= OQmrta Q=}at Q@ |vD@t |=B=m K} QY C}=Oy VwQ '1964 p=U QO '|QJ CyH pQDvm w |}=yv CaQU Q=Okt |R=Uxv}W}@ hOy =@ '= Q |SQv= hqD= |R=Uxv}tm '1989 p=U QO [11] "OQm O=yvW}B lWwt C}=Oy |xrUt |= Q@ '|}=yv CaQU Q=OQ@ QO w [12] 'OQm pL |QDy@ CkO =@ = Q =B=m C}=Oy =@ \@DQt p}Uv=Qi}O |xrO=at 'w= Q C}=Oy QO [13] "OW x=Q= u}r w Twm= QU \UwD xOW|]N |=B=m C}=Oy '1995 p=U |=yQ}eDt T=U= Q@ |r}rLD pL x@ |@=}CUO |R=UxO=U Qw_vtx@ 'xOW|]N |=B=m xD@r= "CU= xOW Q_vhQY OQmrta Q=}at Q}F -=Dsm |=yxrtH R= |O=OaD QF= R= 'Cr=L =@ xU}=kt QO xOWxar=]t OQwt l} |= R= x@ |r}rLD Q=my= Q u}= R= xOt;CUOx@ G}=Dv 1999 p=U QO "CU= xO=O u=Wv = Q |Uwtrt , =D@Uv Cw=iD xrUt u=ty |OOa pL C}=Oy |xrUt Cr=L CqO=at 'u=WD=ar=]t p}tmD |=DU= Q QO [14] 'u}r w Twm= QU |xkrL w |r}rLD pL "OvOQm p}rLD w |UQQ@ |Oa@xU Cr=L QO = Q =B=m |xv}y@ w |}=yv C}akwt Q=OQ@ |=yO}k uDiQo Q_v QO =@ =B=m |xv}y@ C}=Oy |xrUt |xDU@ T=U= 'xOt;CUOx@ |xrO=at "CU= xOW x=Q= [15] u}D@ \UwD |}=yv CaQU Q=OQ@ "CU= xOw@ wrwB; |=t}B=[i C} Qwt -=t QO x=t |xQm |wQ Q@ OwQi C}=Oy |xm@W R= xO=iDU= =@ |v=}t C}=Oy uwv=k '2005 p=U QO 'uH nvw} uQwy Q=m u}= "O=O s}taD =ylWwt QO lQLDt h=Oy= x@ OQwNQ@ CkO Ow@y@ |= Q@ = Q |@Ya V}=Ri= Ea=@ p@=kt QO =t= OwW|t |a=iO |=ylWwt u=wD Q}otWJ V}=Ri= Ea=@ OQmrta OQwt QO |v}=v |r qH '2007 p=U QO [16] "OwW|t R}v C=@U=Lt sHL C}=Oy |=yxQy@ uOW|ov}mD pmWt x@ w= "O=O s=Hv= |r}rLD C}=Oy uwv=k u}= '2007 p=U QO [17] "OQm KQ]t u; KqY= Qw_vtx@ R}v |}=yO=yvW}B w OQm xHwD w =yxJQwt |}xOwD |R=Uxv}y@ sD} Qwor= R= xO=iDU= =@ =B=m C}=Oy uwv=k |R=Uxv}y@ x=Q= [18] |Q=y@wv w '|w@v '`tq uNUwm}v \UwD |OOa |xv}y...…”