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OPTCDEG3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OPTCDEG3
* Problem :
* *********
* An optimal control problem determining the applied force
* that restores a cubically damped spring-mass system to equilibrium
* as fast as possible, given bounds on state and control variables.
* The displacement of the mass from equilibrium is x, velocity is y,
* and the controlling force is u. The objective function also differs
* slightly from that of OPTCDEG2.
* Source:
* P.S. Ritch,
* Automatica, 1973, V9, pp 415-429,
* (example 6.1)
* SIF input: Todd Plantenga, August 1995.
* classification QQR2-AN-V-V
* problem size: 3T+2 unknowns, T nonlinear equalities
*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
* useful parameters
IA T-1 T -1
RI TMP T
RD DT TMP 20.0
RM MINUSDT DT -1.0
RM A1 DT 0.1
RE SPRINGKM 0.02
RE DAMPING 0.05
R* C1 SPRINGKM DT
R* C2 DAMPING DT
IE 0 0
IE 1 1
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
ZE B(t) y(t) MINUSDT
XE C(t) y(t+1) 1.0 y(t) -1.0
ZE C(t) u(t) MINUSDT
ZE C(t) x(t) C1
ND
BOUNDS
DO t 0 T-1
XR OPTCDEG3 x(t)
XL OPTCDEG3 y(t) -1.0
XL OPTCDEG3 u(t) -0.2
XU OPTCDEG3 u(t) 0.2
ND
XX OPTCDEG3 x(0) 10.0
XX OPTCDEG3 x(T) 0.0
XX OPTCDEG3 y(0) 0.0
XR OPTCDEG3 y(T)
START POINT
DO t 1 T-1
X OPTCDEG3 y(t) -1.0
ND
ELEMENT TYPE
EV SQR X
EV CUBE X
ELEMENT USES
DO t 0 T
XT o(t) SQR
ZV o(t) X x(t)
ND
XT oy SQR
ZV oy X y(T)
DO t 0 T-1
XT c(t) CUBE
ZV c(t) X y(t)
ND
GROUP USES
DO t 0 T
ZE OBJ o(t) A1
ND
XE OBJ oy 1000.0
DO t 0 T-1
ZE C(t) c(t) C2
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO OPTCDEG3 0.0
* Solution
*LO SOLTN 67.4677 (T= 10) Y( 2) thru Y( 4) have active lower bound
*LO SOLTN 50.6341 (T= 40) Y( 6) thru Y( 18) have active lower bounds
*LO SOLTN 47.6146 (T=100) Y(14) thru Y( 45) have active lower bounds
*LO SOLTN 46.145 (T=400) Y(53) thru Y(181) have active lower bounds
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OPTCDEG3
INDIVIDUALS
* square element.
T SQR
F X * X
G X X + X
H X X 2.0
* cube element.
T CUBE
F X * X * X
G X 3.0 * X * X
H X X 6.0 * X
ENDATA