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OPTCTRL6.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OPTCTRL6
* Problem :
* *********
* An optimal control problem
* This problem is a modification of OPTCNTRL. All bound constraints
* were removed. At the solution, the bounds on U1-U9 are active,
* so a penalty term was added to the objective:
*
* mu * ||u(i) - active_bound||
*
* The value of mu (TDP_mu) was chosen to be very large, making the
* Hessian of the objective ill-conditioned.
* Source:
* B. Murtagh and M. Saunders,
* Mathematical Programming studies 16, pp 84-117,
* (example 5.11)
* SIF input: Nick Gould, June 1990.
* modified by T. Plantagena, December 1992.
* classification QQR2-AN-V-V
* useful parameters
*IE T 10 $-PARAMETER n = 32
*IE T 40 $-PARAMETER n = 122 original value
*IE T 100 $-PARAMETER n = 302
*IE T 400 $-PARAMETER n = 1202
IE T 1500 $-PARAMETER n = 4502
IA T-1 T -1
IE 0 0
IE 1 1
* penalty parameter mu
RE TDP_mu 1.0D+6
VARIABLES
DO t 0 T
X x(t)
X y(t)
ND
DO t 0 T-1
X u(t)
ND
GROUPS
N OBJ
DO t 0 T-1
IA t+1 t 1
XE B(t) x(t+1) 1.0 x(t) -1.0
XE B(t) y(t) -0.2
XE C(t) y(t+1) 1.0 y(t) -1.0
XE C(t) x(t) 0.004 u(t) -0.2
ND
BOUNDS
DO t 0 T-1
XR OPTCTRL6 x(t)
XR OPTCTRL6 y(t)
XR OPTCTRL6 u(t)
ND
XX OPTCTRL6 x(0) 10.0
XR OPTCTRL6 x(T)
XX OPTCTRL6 y(0) 0.0
XX OPTCTRL6 y(T) 0.0
START POINT
DO t 1 T-1
X OPTCTRL6 y(t) -1.0
ND
ELEMENT TYPE
EV SQR X
EV SQR_TDP X
ELEMENT USES
DO t 0 T
XT o(t) SQR
ZV o(t) X x(t)
ND
DO t 1 T-1
XT o_TDP(t) SQR_TDP
ZV o_TDP(t) X u(t)
ND
DO t 0 T-1
XT c(t) SQR
ZV c(t) X y(t)
ND
GROUP USES
DO t 0 T
XE OBJ o(t) 0.5
ND
DO t 1 T-1
ZE OBJ o_TDP(t) TDP_mu
ND
DO t 0 T-1
XE C(t) c(t) 0.01
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO OPTCRTL6 0.0
* Solution
*LO SOLTN 2048.00 (T=40)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OPTCTRL6
TEMPORARIES
R X_TDP
INDIVIDUALS
* square element.
T SQR
F X * X
G X X + X
H X X 2.0
T SQR_TDP
A X_TDP X - 0.2
F X_TDP * X_TDP
G X X_TDP + X_TDP
H X X 2.0
ENDATA