ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2014. Vol. 8

Numerical Methods for Calculation of Time-Optimal Control

A. I. Tyatyushkin
The article is devoted to algorithms for calculation of time-optimal control in the linear systems. Proposed set of algorithms make possible apply multi-method technique to solving time-optimal control problems with different singularity. Corresponding to this technology the solution is found by a multimethods’ algorithm consisting of a sequence of steps of different methods applied to the optimization process in order to accelerate it. Such a technology allows to consider some particularities of the problem of interest at all stages of its solution and to improve the efficiency of optimal control search.
convex hull method, attainability set, time-optimal problem, minimax algorithm, linear controlled system

1. Andreev N. Manage finite linear objects (in Russian). Moscow, Nauka 1976, 424 p.

2. Vasil’ev O.V., Tyatyushkin A.I. On the numerical solution of linear time-optimal control (in Russian). Differential and Integral Equations. Irkutsk, University Press, 1973, issue 2, pp. 57–69.

3. Gabasov R., Kirillova F.M. Qualitative theory of optimal processes (in Russian). Moscow, Nauka, 1971, 508 p.

4. Gabasov R., Kirillova F.M., Tyatyushkin A.I. Constructive Optimization Methods. Part 1: Linear problems (in Russian). Minsk, 1984, 214 p.

5. Kalman R., Falb P., Arbib M. Essays on mathematical systems theory. New York, Wiley, 1971 . 400 p.

6. Krasovskii N.N. Theory of motion control (in Russian). Moscow, Nauka, 1968, 476 p.

7. Tyatyushkin A.I., Fedunov B.E. Numerical study of the properties of optimal control in a pursuit problem (in Russian). Math. RAS, Tisza. 2005, no. 3, pp. 104–113.

8. Tyatyushkin A.I. Multimethod optimization technology controlled systems (in Russian). Novosibirsk, Nauka, 2006, 343 p.

9. Barr R.O. An efficient computational procedure for a generalized quadratic programming problem. J.SIAM Control, 1969, vol. 7, no. 3, pp. 415–429.

10. Eaton J.H. An iterative solution to time-optimal control. J. Math. Anal. and Appl., 1962, vol. 5, no. 2, p. 329–344.

11. Gibert E.G. An iterative procedure for computing the minimum of a quadratic from on a convex set. J. SIAM Control, 1966, vol. 4, no. 1, pp. 61–80.

12. Tyatyushkin A.I. A multimethod technique for solving optimal control problem. Optimization Letters, 2012, vol. 7, pp. 1335–1347.

Full text (russian)