A new procedure for optimization of linear time-varying dynamic systems has been proposed that uses transformations to embed the dynamic equations explicitly into the cost functional. This leads to elimination of Lagrange multipliers and characterization of the optimality equations by high-order differential equations in the same number of variables as number of control inputs. This procedure requires that the transformation matrix be nonsingular at all time within the domain. This paper extends this procedure to problems where a single nonsingular transformation matrix does not exist over the entire domain. In this paper, the time domain is partitioned into intervals such that a nonsingular transformation exists over each interval. The transformations are used to embed the dynamic equations into the cost functional. Variational analysis of the unconstrained cost functionals results in the optimality equations, which are solved efficiently by weighted residual methods. [S0739-3717(00)00601-2]

Issue Section:
Technical Papers
Keywords:
time-varying systems, linear systems, optimisation, variational techniques, state-space methods
Topics:
Boundary-value problems, Dynamic systems, Optimization, Computation, Differential equations, Equations of motion
1.
Kirk, D. E., 1970, Optimal Control Theory: An Introduction, Prentice Hall Electrical Engineering Series, Englewood Cliffs, NJ.
2.
Bryson, A. E., and Ho, Y. C., 1975, Applied Optimal Control, Hemisphere Publishing Company, Washington.
3.
Agrawal
,
S. K.
, and
Veeraklaew
,
T.
,
1996
, “
A Higher-Order Method for Dynamic Optimization of a Class of Linear Time-Invariant Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
118
, No.
4
, pp.
786
–
791
.
4.
Agrawal
,
S. K.
, and
Xu
,
X.
,
1997
, “
A New Procedure for Optimization of a Class of Linear Time-Varying Dynamic Systems
,”
J. Vibr. Control
,
3
, No.
4
, pp.
379
–
396
.
5.
Gelfand, I. S., and Fomin, S. V., 1963, Calculus of Variations, Prentice-Hall Book Company, Englewood Cliffs, NJ.
6.
Pinch, E. R., 1993, Optimal Control and the Calculus of Variations, Oxford University Press, New York.
7.
Brebbia, C. A., 1978. The Boundary Element Method for Engineers, Pentech Press, London.
8.
Fletcher, C. A. J., 1984, Computational Galerkin Methods, Springer Verlag, New York.
9.
Xu, X., 1999, New Approaches to Optimization of Linear Time-Varying Systems and Classes of Nonlinear Dynamic Systems, Ph.D. Thesis, Department of Mechanical Engineering, University of Delaware, Newark, DE.
Copyright © 2000
 by ASME
You do not currently have access to this content.