In a series of papers [1, 2], A. M. Letov discussed an optimal regulator problem for a linear plant with bounded control variable and quadratic performance index. This problem was also discussed by Chang . Krasovskii and Letov observed later  that the solution proposed in [1, 2, and 3] may be correct only for special choices of the initial value of the state vector. In the present note, further aspects of the solution in the general case are described and three examples are given. The possible existence of a regime of unsaturated-nonlinear optimal control is demonstrated. The presence of this regime in the optimal control law was apparently overlooked in [1–4].
On a Problem of Letov in Optimal Control
C. D. Johnson,
C. D. Johnson
Electrical Engineering Department, University of Alabama, Huntsville Center, Huntsville, Ala.
W. M. Wonham
Center for Control Theory, RIAS, Baltimore, Md.
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Johnson, C. D., and Wonham, W. M. (March 1, 1965). "On a Problem of Letov in Optimal Control." ASME. J. Basic Eng. March 1965; 87(1): 81–89. https://doi.org/10.1115/1.3650531
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