Cite this article as:
Grebennikova I. V., Kremlev A. G. Iterative Procedure of Constructing Optimal Solving in the Minimax Problem of Control for Singularly Perturbed System with Delay with Geometric Constraints. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2016, vol. 16, iss. 3, pp. 272-280. DOI: https://doi.org/10.18500/1816-9791-2016-16-3-272-280
Iterative Procedure of Constructing Optimal Solving in the Minimax Problem of Control for Singularly Perturbed System with Delay with Geometric Constraints
The control problem for the singularly perturbed system with delay with indeterminate initial conditions and geometric constraints on the control resources according to the minimax criterion is considered. Iterative procedure of constructing control response that approximates the optimal solution with given accuracy with respect to a small positive parameter is proposed.
1. Krasovskii N. N. Teorija upravlenija dvizheniem [The Theory of Motion Control]. Moscow, Nauka, 1968, 475 p. (in Russian).
2. Kurzhanskij A. B. Upravlenie i nabljudenie v uslovijah neopredelennosti [Control and Observation under the Uncertainty Conditions]. Moscow, Nauka, 1977, 392 p. (in Russian).
3. Kremlev A. G. Asymptotic properties of a set of trajectories of a singularly perturbed system in the optimal control problem. Autom. Remote Control, 1993, vol. 54, no. 9, pp. 1353–1367.
4. Grebennikova I. V. Solution approximation in a minimax control problem for a singularly perturbed system with delay. Russian Math., 2011, vol. 55, no. 10, pp. 23–33. DOI: https://doi.org/10.3103/S1066369X11100045.
5. Grebennikova I. V., Kremlev A. G. Approximation of control for singularly perturbed system with delay with geometric constraints. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2015, vol. 15, iss. 2, pp. 142–151 (in Russian). DOI: https://doi.org/10.18500/1816-9791-2015-15-2-142-151.
6. Rokafellar R. Vypuklyj analiz [Convex Analysis]. Moscow, Mir, 1973, 492 p. (in Russian).
7. Krasovskii N. N. Nekotorye zadachi teorii ustojchivosti dvizhenija [Some Problems in the Theory of Stability of Motion]. Moscow, Fizmatgiz, 1959, 468 p. (in Russian).
8. Natanson I. P. Teorija funkcij veshhestvennoj peremennoj [Theory of Functions of a Real Variable]. Moscow, Nauka, 1974, 468 p. (in Russian).
9. Grebennikova I. V. On iterative method of constructing optimal control for singularly perturbed systems with delay. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2009, vol. 9, iss. 3, pp. 14–22 (in Russian).
10. Kirillova F. M. Relative controllability of linear dynamic systems with delay. Doklady AN SSSR, 1967, vol. 174, no. 6, pp. 1260–1263 (in Russian).