# On Target Control Synthesis Under Set-Membership Uncertainties Using Polyhedral Techniques

Elena Kostousova^{*}

Problems of terminal target feedback control for linear and bilinear differential systems without and with uncertainties are considered. There are known approaches to solving problems like these based on construction of solvability tubes. Since their practical construction may be cumbersome, the different numerical methods are devised for this cause. Among them computation schemes for linear systems using an ellipsoidal technique were proposed by A.B.Kurzhanski and then expanded to a polyhedral technique by the author. Here we continue the development of polyhedral control synthesis using polyhedral (parallelotope-valued) solvability tubes. We deal with two types of problems: when controls are additive and when they are involved into the system matrix. For both problems, the cases without uncertainties, with additive parallelotope-valued uncertainties, and also with a bilinear uncertainty (interval uncertainties in coefficients of the system) are considered. Ordinary differential equations, which describe the mentioned polyhedral solvability tubes, are presented for each of these cases. New control strategies, which can be calculated by explicit formulas on the base of the mentioned tubes, are proposed. Results of computer simulations are presented.

Mathematics Subject Classification: 93C15 93C41 65G40 65D99

Keywords: Differential systems; uncertain systems; control synthesis; polyhedral estimates; parallelotopes; interval analysis

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