×

The controllability of an interval linear discrete system. (English. Russian original) Zbl 1297.93032

J. Comput. Syst. Sci. Int. 46, No. 3, 399-406 (2007); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upr. 2007, No. 3, 67-74 (2007).
Summary: A linear discrete control system with variable interval coefficients is considered. We investigate the controllability of the system, i.e. the possibility of steering its trajectory bundle from one given slab to another for a finite number of steps using the appropriate control. Necessary and sufficient conditions of controllability in the form of solvability of a linear programming problem are obtained. The optimal plan for the problem is given by the control that steers the trajectory bundle of the system from the initial slab into the minimal neighborhood of a finite slab.

MSC:

93B05 Controllability
93C55 Discrete-time control/observation systems
93C41 Control/observation systems with incomplete information
65G30 Interval and finite arithmetic
90C05 Linear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yu. M. Gusev, V. N. Efanov, V. G. Krymskii, and V. Yu. Rutkovskii, ”Analysis and Synthesis of Linear Interval Dynamic Systems (State of the Art)). I, II,” Izv. Ross. Akad. Nauk, Tekh. Kibern., No. 2, 3–30 (1991).
[2] A. B. Kurzhanskii, Control and Observation under Conditions of Uncertainty (Nauka, Moscow, 1977) [in Russian].
[3] M. H. A. Davis, Linear Estimation and Stochastic Control (Chapman and Hall, London 1977; Mir, Moscow, 1984). · Zbl 0437.60001
[4] F. L. Chernous’ko, Estimation of the Phase State of Dynamic Systems (Nauka, Moscow, 1988) [in Russian].
[5] N. E. Kirin, Methods of Estimation and Control in Dynamic Systems (St.-Petersb. Gos. Univ., St. Petersburg, 1993) [in Russian].
[6] R. E. Kalman, P. L. Falb, and M. A. Arbib, Topics in Mathematical System Theory (Mc Graw-Hill, New York, 1969; Mir, Moscow, 1971). · Zbl 0231.49001
[7] N. N. Krasovskii, The Theory of Motion Control (Nauka, Moscow, 1968) [in Russian].
[8] R. F. Gabasov and F. M. Kirillova, Optimization of Linear Systems (Belorus. Gos. Univ., Minsk, 1973) [in Russian].
[9] F. P. Vasil’ev and A. Yu. Ivanitskii, Linear Programming (Faktorial, Moscow, 1998) [in Russian].
[10] B. S. Dobronets and V. V. Shaidurov, Two-Sided Numerical Methods (Nauka, Novosibirsk, 1990) [in Russian].
[11] L. T. Ashchepkov and D. V. Davydov, ”Stabilization of an Observable Linear Control System with Constant Interval Coefficients,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 11–17 (2002). · Zbl 1062.93033
[12] F. R. Gantmakher, The Theory of Matrices (Nauka, Moscow, 1967) [in Russian]. · Zbl 0050.24804
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.