The focus of this paper is on the design of robust input shapers where the maximum value of the cost function over the domain of uncertainty is minimized. This nonlinear programming problem is reformulated as a linear programming problem by approximating a n-dimensional hypersphere with multiple hyperplanes (as in a geodesic dome). A recursive technique to approximate a hypersphere to any level of accuracy is developed using barycentric coordinates. The proposed technique is illustrated on the spring-mass-dashpot and the benchmark floating oscillator problem undergoing a rest-to-rest maneuver. It is shown that the results of the linear programming problem are nearly identical to that of the nonlinear programming problem.

1.
Smith
,
O. J. M.
, 1957, “
Posicast Control of Damped Oscillatory Systems
,”
Proc. IRE
0096-8390,
45
(
9
), pp.
1249
1255
.
2.
Singer
,
N. C.
, and
Seering
,
W. P.
, 1990, “
Preshaping Command Inputs to Reduce System Vibrations
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
112
, pp.
76
82
.
3.
Swigert
,
C. J.
, 1980, “
Shaped Torque Techniques
,”
J. Guid. Control
0162-3192,
3
, pp.
460
467
.
4.
Singh
,
T.
, and
Vadali
,
S. R.
, 1993, “
Robust Time-Delay Control
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
112
(
2A
), pp.
303
306
.
5.
Singh
,
T.
, and
Vadali
,
S. R.
, 1995, “
Robust Time-Delay Control of Multimode Systems
,”
Int. J. Control
0020-7179,
62
(
6
), pp.
1319
1339
.
6.
Singhose
,
W.
,
Derezinski
,
S.
, and
Singer
,
N.
, 1996, “
Extra-Insensitive Input Shapers for Controlling Flexible Spacecraft
,”
J. Guid. Control Dyn.
0731-5090,
19
, pp.
385
91
.
7.
Singh
,
T.
, 2002, “
Minimax Design of Robust Controllers for Flexible Systems
,”
J. Guid. Control Dyn.
0731-5090,
25
(
5
), pp.
868
875
.
8.
Singh
,
T.
, and
Vadali
,
S. R.
, 1994, “
Robust Time-Optimal Control: A Frequency Domain Approach
,”
J. Guid. Control Dyn.
0731-5090,
17
(
2
), pp.
346
353
.
9.
Vanderbei
,
R. J.
, 2001,
Linear Programming: Foundations and Extensions
,
2nd ed.
,
Springer
,
New York
.
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