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JUNKTURN.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME JUNKTURN
* Problem :
* *********
* The spacecraft orientation problem by Junkins and Turner. This is a
* nonlinear optimal control problem.
* The problem is not convex.
* Source:
* A.I Tyatushkin, A.I. Zholudev and N. M. Erinchek,
* "The gradient method for solving optimal control problems with phase
* constraints",
* in "System Modelling and Optimization", P. Kall, ed., pp. 456--464,
* Springer Verlag, Lecture Notes in Control and Information Sciences 180, 1992.
* This reference itself refers to:
* I.L. Junkins and I.D. Turner,
* "Optimal continuous torque attitude maneuvers",
* AIAA/AAS Astrodynamics Conference, Palo Alto, 1978.
* SIF input: Ph. Toint, February 1994.
* classification QQR2-MN-V-V
* Number of discretized points in [0,100] - 1.
* The number of variables is 10 * ( N + 1 )
* The number of constraints is 7 * N
* N should be large enough to ensure feasibility.
*IE N 50 $-PARAMETER n = 510, m = 350
*IE N 100 $-PARAMETER n = 1010, m = 700
*IE N 500 $-PARAMETER n = 5010, m = 3500
IE N 1000 $-PARAMETER n = 10010, m = 7000
* Mesh
IA N-1 N -1
RI RN N
RD H RN 100.0
RM H/2 H 0.5
RM 6H/5 H 1.2
RM SH H 1.0909
RM S1H H -0.08333
RM S2H H 0.18182
RM -H/2 H -0.5
RM -H H -1.0
RM -H/10 H -0.1
RM H/4 H 0.25
* Constants
IE 0 0
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
IE 6 6
IE 7 7
VARIABLES
* State variables
DO I 1 7
DO T 0 N
X X(I,T)
OD T
OD I
* Control variables
DO I 1 3
DO T 0 N
X U(I,T)
OD T
OD I
GROUPS
* Objective function
XN OBJ
* State constraints
DO T 1 N
IA T-1 T -1
DO I 1 7
XE C(I,T) X(I,T) -1.0 X(I,T-1) 1.0
OD I
ZE C(5,T) U(1,T) H
ZE C(6,T) U(2,T) 6H/5
ZE C(7,T) U(3,T) SH
ND
BOUNDS
FR JUNKTURN 'DEFAULT'
XX JUNKTURN X(1,0) 1.0
XX JUNKTURN X(2,0) 0.0
XX JUNKTURN X(3,0) 0.0
XX JUNKTURN X(4,0) 0.0
XX JUNKTURN X(5,0) 0.01
XX JUNKTURN X(6,0) 0.005
XX JUNKTURN X(7,0) 0.001
XX JUNKTURN X(1,N) 0.43047
XX JUNKTURN X(2,N) 0.70106
XX JUNKTURN X(3,N) 0.0923
XX JUNKTURN X(4,N) 0.56098
XX JUNKTURN X(5,N) 0.0
XX JUNKTURN X(6,N) 0.0
XX JUNKTURN X(7,N) 0.0
START POINT
XV JUNKTURN 'DEFAULT' 1.0
XV JUNKTURN X(1,0) 1.0
XV JUNKTURN X(5,0) 0.01
XV JUNKTURN X(6,0) 0.005
XV JUNKTURN X(7,0) 0.001
XV JUNKTURN X(1,N) 0.43047
XV JUNKTURN X(2,N) 0.70106
XV JUNKTURN X(3,N) 0.0923
XV JUNKTURN X(4,N) 0.56098
ELEMENT TYPE
EV 2PR V W
EV SQ V
ELEMENT USES
* Objective function elements
DO T 0 N
XT U1S(T) SQ
ZV U1S(T) V U(1,T)
XT U2S(T) SQ
ZV U2S(T) V U(2,T)
XT U3S(T) SQ
ZV U3S(T) V U(3,T)
OD T
* State constraints elements
DO T 1 N
XT P15(T) 2PR
ZV P15(T) V X(1,T)
ZV P15(T) W X(5,T)
XT P16(T) 2PR
ZV P16(T) V X(1,T)
ZV P16(T) W X(6,T)
XT P17(T) 2PR
ZV P17(T) V X(1,T)
ZV P17(T) W X(7,T)
XT P25(T) 2PR
ZV P25(T) V X(2,T)
ZV P25(T) W X(5,T)
XT P26(T) 2PR
ZV P26(T) V X(2,T)
ZV P26(T) W X(6,T)
XT P27(T) 2PR
ZV P27(T) V X(2,T)
ZV P27(T) W X(7,T)
XT P35(T) 2PR
ZV P35(T) V X(3,T)
ZV P35(T) W X(5,T)
XT P36(T) 2PR
ZV P36(T) V X(3,T)
ZV P36(T) W X(6,T)
XT P37(T) 2PR
ZV P37(T) V X(3,T)
ZV P37(T) W X(7,T)
XT P45(T) 2PR
ZV P45(T) V X(4,T)
ZV P45(T) W X(5,T)
XT P46(T) 2PR
ZV P46(T) V X(4,T)
ZV P46(T) W X(6,T)
XT P47(T) 2PR
ZV P47(T) V X(4,T)
ZV P47(T) W X(7,T)
XT P56(T) 2PR
ZV P56(T) V X(5,T)
ZV P56(T) W X(6,T)
XT P57(T) 2PR
ZV P57(T) V X(5,T)
ZV P57(T) W X(7,T)
XT P67(T) 2PR
ZV P67(T) V X(6,T)
ZV P67(T) W X(7,T)
OD T
GROUP USES
* Objective function
ZE OBJ U1S(0) H/4
DO T 1 N-1
ZE OBJ U1S(T) H/2
ZE OBJ U2S(T) H/2
ZE OBJ U3S(T) H/2
OD T
ZE OBJ U1S(N) H/4
* State constraints
DO T 1 N
ZE C(1,T) P25(T) -H/2
ZE C(1,T) P36(T) -H/2
ZE C(1,T) P47(T) -H/2
ZE C(2,T) P15(T) H/2
ZE C(2,T) P37(T) H/2
ZE C(2,T) P46(T) -H/2
ZE C(3,T) P16(T) H/2
ZE C(3,T) P27(T) -H/2
ZE C(3,T) P45(T) H/2
ZE C(4,T) P17(T) H/2
ZE C(4,T) P26(T) H/2
ZE C(4,T) P35(T) -H/2
ZE C(5,T) P67(T) S1H
ZE C(6,T) P57(T) -H/10
ZE C(7,T) P56(T) S2H
OD T
OBJECT BOUND
LO JUNKTURN 0.0
* Solution
*LO SOLTN(500) 7.417771100D-5
*LO SOLTN(1000) 1.224842784D-5
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
ELEMENTS JUNKTURN
INDIVIDUALS
T 2PR
F V * W
G V W
G W V
H V W 1.0
T SQ
F V * V
G V V + V
H V V 2.0
ENDATA