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Equivalence of regularizations in abstract problems with different classes of admissible controls

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Conclusion

Theorems 4.1, 4.2 and 6.1, 6.2 respectively admit a natural specialization for the problem of constructing the reachability region of the linear controlled system from Sec. 1. Informally, this specialization has the following form. If the vector functions b(·) and S(·) from Sec. 1 are “not too discontinuous” (admit a uniform approximation by piecewise-constant and right-continuous maps on [t0, voD, then, given a common resource constraintc, the controlled analogues of reachability regions are identical for the class of controls with an integral constraint (on the total pulse) and the class of “pure pulse” shock controls, whereas the “ordinary” reachability regions corresponding to unperturbed conditions (see, e.g., they− constraint in (1.2)) may be different. This is illustrated by the examples of Sees. 1, 5. The regularized version of the problem of constructing the reachability region of a linear system is thus insensitive to a change of the class of admissible controls.

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Authors
  1. Yu. I. Berdyshev
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  2. A. G. Chentsov
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Additional information

The study was supported by the Russian Foundation for Basic Research (94-01-00350).

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–17, May–June, 1998.

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Berdyshev, Y.I., Chentsov, A.G. Equivalence of regularizations in abstract problems with different classes of admissible controls. Cybern Syst Anal 34, 377–385 (1998). https://doi.org/10.1007/BF02666979

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