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| Problems of feedback terminal target control for linear dynamical discrete-time systems without and with uncertainties are considered. There are known approaches to solving problems of this kind, including ones for differential systems, based on construction of solvability tubes. Since practical construction of such tubes may be cumbersome, the different numerical methods are devised. Among them computation schemes for linear systems based on the ellipsoidal techniques were proposed by A.B.~Kurzhanski and then expanded to the polyhedral techniques by the author.
Here we continue the development of methods of control synthesis for discrete-time systems using polyhedral (parallelotope-valued) solvability tubes. The cases without uncertainties, with additive parallelotope-valued uncertainties, and also with interval uncertainties in coefficients of the system are considered. Also polyhedral methods of control synthesis for the same systems under constraints on the state are proposed. The state constraints are described in terms of zones (i.e., intersections of strips). Control strategies, which can be calculated by explicit formulas on the base of polyhedral solvability tubes, are proposed. Recurrence relations, which describe the mentioned tubes, are presented for each of the mentioned cases. Results of computer simulations are presented. |
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