In a previous paper (Hampton, R. D., et al., 1996, “A Practical Solution to the Deterministic Nonhomogeneous LQR Problem,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 118, pp. 354–360.) the authors presented a solution to the nonhomogeneous linear-quadratic-regulator (LQR) problem, for the case of known, deterministic, persistent (“non-dwindling”) disturbances. The authors used variational calculus and state-transition-matrix methods to produce an optimal matric solution, for bounded determinist forcing terms. A restricted version of this problem (treating dwindling disturbances) was evidently first investigated by Salukvadze, M. E., 1962, “Analytic Design of Regulators (Constant Disturbance),” Automation and Remote Control, Vol. 22, No. 10, Mar., pp. 1147–1155, using a differential-equations approach. The present paper uses Salukvadze’s approach to extend his work to the case of non-dwindling disturbances, with cross-weightings between state- and control vectors, and pursues the solution to the same form reported previously in Hampton et al.

1.
Salukvadze
,
M. E.
,
1962
, “
Analytic Design of Regulators (Constant Disturbances)
,”
Automation and Remote Control
,
22
, No.
10
, Mar, pp.
1147
1155
;
2.
Originally published in
Avtomatika i Telemakhanika
,
22
, No.
10
, Oct.
1961
, pp.
1279
1287
.
1.
Hampton
,
R. D.
,
Knospe
,
C. R.
, and
Townsend
,
M. A.
,
1996
, “
A Practical Solution to the Deterministic Nonhomogeneous LQR Problem
,”
ASME J. Dyn. Syst., Meas., Control
,
118
, pp.
354
360
.
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