N.M. Dmitruk. Multiply closed control strategy in a linear terminal problem of optimal guaranteed control ... P. 66-82

This paper deals with an optimal control problem for a linear discrete system with disturbances. It is required to steer the system robustly to a given terminal set in a finite time while minimizing the guaranteed value of a terminal cost function. A multiply closed control strategy is introduced; it takes into account the assumption that, at several future times, the state of the system will be measured exactly and the control input will be corrected. An efficient numerical method for constructing a suboptimal multiply closed strategy is proposed. The results of numerical experiments show an improvement in the performance under the optimal control strategy when the number of closing instants increases as well as in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.

Keywords: linear system, disturbances, robust optimal control, control strategy, algorithm

Received June 1, 2022

Revised July 15, 2022

Accepted July 18, 2022

Funding Agency: This work was supported by the National Program for Scientific Research of the Republic of Belarus “Convergence 2025” (project no. 1.2.04.1).

Natalia Mikhailovna Dmitruk, Cand. Sci. ( Phys.-Math.), Belarusian State University, Minsk, 220030 Belarus, e-mail: dmitrukn@bsu.by

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Cite this article as: N.M. Dmitruk. Multiply closed control strategy in a linear terminal problem of optimal guaranteed control. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 3, pp. 66–82; Proceedings of the Steklov Institute of Mathematics (Suppl.), 2022, Vol. 319, Suppl. 1, pp. S112–S128.