Abstract
In a linear control system over a fixed time interval, we treat steering to the origin by controls (i) having realistic constraints on their values, while minimizing theL 1-cost of control, (ii) without such constraints, and (iii) minimizing the coordinate bound, with or without a givenL 1-cost restriction. Existence (also, nonexistence) results are obtained, together with further necessary conditions for control optimality.
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Communicated by G. Leitmann
The author was introduced to these problems by Professors P. Hagedorn and W. Krabs and profited much by discussions with them and with other workers at the TH Darmstadt. The incisive idea that feedback controls still exist if state space is augmented by one dimension (see Example, Section 1) is due to Professor Hagedorn and obviously merits further treatment. Professor E. N. Chukwu pointed out an error in a preprint version of this paper, and the present formulation of Theorem 4.6 is the result of discussions with him. In a colloquium at Würzburg University, Professor P. C. Parks made the point that a portion ofmodern control theory is implicit in the work of Achiezer: in connection with the present material, the so-called M-moment problem, and our Theorem 4.6. The referee kindly pointed out the reference for the example in Section 1. This paper is a revised version of a report, Preprint No. 279, prepared while the author held a Humboldt Award at the TH Darmstadt.
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Hájek, O. L 1-optimization in linear systems with bounded controls. J Optim Theory Appl 29, 409–436 (1979). https://doi.org/10.1007/BF00933143
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DOI: https://doi.org/10.1007/BF00933143