Control problems in dynamic systems require an optimal selection of input trajectories and system parameters. In this paper, a novel procedure for optimization of a linear dynamic system is proposed that simultaneously solves the parameter design problem and the optimal control problem using a specific system state transformation. Also, the proposed procedure includes structural design constraints within the control system. A direct optimal control method is also examined to compare it with the proposed method. The limitations and advantages of both methods are discussed in terms of the number of states and inputs. Consequently, linear dynamic system examples are optimized under various constraints and the merits of the proposed method are examined.

References

References
1.
Kirk
,
D. E.
,
1970
,
Optimal Control Theory: An Introduction
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
2.
Oz
,
H.
, and
Adiguzel
,
E.
,
1995
, “
Hamilton's Law of Varying Action. Part II: Direct Optimal Control of Linear Systems
,”
J. Sound Vib.
,
179
(
4
), pp.
711
724
.10.1006/jsvi.1995.0046
3.
Chen
,
C.
, and
Hsiao
,
C.
,
1975
, “
Design of Piecewise Constant Gains for Optimal Control via Walsh Functions
,”
IEEE Trans. Autom. Control
,
20
(
5
), pp.
596
603
.10.1109/TAC.1975.1101057
4.
Kekkeris
,
G. T.
, and
Paraskevopoulos
,
P. N.
,
1988
, “
Hermite Series Approach to Optimal Control
,”
Int. J. Control
,
47
(
2
), pp.
557
567
.10.1080/00207178808906031
5.
Agrawal
,
S. K.
, and
Veeraklaew
,
T.
,
1996
, “
A Higher-Order Method for Dynamic Optimization of a Class of Linear Systems
,”
ASME J. Dyn. Syst.
,
Meas. Control
,
118
(
4
), pp.
786
791
.10.1115/1.2802358
6.
Agrawal
,
S. K.
, and
Xu
,
X.
,
1997
, “
A New Procedure for Optimization of a Class of Linear Time-Varying Dynamic Systems
,”
J. Vib. Control
,
3
(
4
), pp.
379
396
.10.1177/107754639700300401
7.
Williamson
,
W. E.
,
1971
, “
Use of Polynomial Approximations to Calculate Suboptimal Controls
,”
AIAA J.
,
9
(
11
), pp.
2271
2273
.10.2514/3.6499
8.
Stryk
,
O. V.
, and
Bulirsch
,
R.
,
1992
, “
Direct and Indirect Methods for Trajectory Optimization
,”
Ann. Oper. Res.
,
37
(
1
), pp.
357
373
.10.1007/BF02071065
9.
Hargraves
,
C. R.
, and
Paris
,
S. W.
,
1987
, “
Direct Trajectory Optimization Using Nonlinear Programming and Collocation
,”
J. Guid. Control Dyn.
,
10
(
4
), pp.
338
342
. 10.2514/3.20223
10.
Butcher
,
J. C.
,
2003
,
Numerical Methods for Ordinary Differential Equaions
,
John Wiley & Sons
,
Chichester
, UK.
11.
Jung
,
U. J.
,
Park
,
G. J.
, and
Agrawal
,
S. K.
,
2011
, “
Parameter Design in Optimal Control Problems for Linear Dynamic Systems Using a Canonical Form
,”
ASME 2011 Dynamic Systems and Control Conference
, pp. 621–62810.1115/DSCC2011-6056.
12.
Sira-Ramirez
,
H.
, and
Agrawal
,
S. K.
,
2004
,
Differentially Flat Systems
,
Marcel Dekker
, Inc.,
New York
.
13.
Kailath
,
T.
,
1980
,
Linear Systems
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
14.
Park
,
G. J.
,
2007
,
Analytical Methods for Design Practice
,
Springer
,
London
.
15.
Arora
,
J. S.
,
1989
,
Introduction to Optimum Design
,
McGraw-Hill
,
New York
.
16.
Franch
,
J.
,
Agrawal
,
S. K.
, and
Sangwan
,
V.
,
2010
, “
Differential Flatness of a Class of n-DOF Planar Manipulators Driven by 1 or 2 Actuators
,”
IEEE Trans. Autom. Control
,
55
(
2
), pp.
548
554
.10.1109/TAC.2009.2037480
17.
Korayem
,
M. H.
, and
Nikoobin
,
A.
,
2008
, “
Maximum Payload for Flexible Joint Manipulators in Point-to-Point Task Using Optimal Control Appoach
,”
Int. J. Adv. Manuf. Technol.
,
38
(
9-10)
, pp.
1045
1060
.10.1007/s00170-007-1137-2
18.
Taylor
,
J. E.
, and
Bendsoe
,
M. P.
,
1984
, “
An Interpretation for Min-Max Structural Design Problems Including a Method for Relaxing Constraints
,”
Int. J. Solids Struct.
,
20
(
4
), pp.
301
314
.10.1016/0020-7683(84)90041-6
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