This paper deals with an optimal control problem for a linear discrete-time system subject to unknown bounded disturbance. It is required to steer the system robustly to a terminal set with the smallest total impulse of the control function. A problem of constructing an optimal multiply closed control strategy is formulated. It is assumed that the system states are measured and the control is corrected at some future times. A method for calculating an optimal strategy based on reducing the formulated problems to linear programs is proposed.
Keywords: linear system, disturbances, robust optimal control, control strategy, algorithm
Received April 4, 2024
Revised May 1, 2024
Accepted May 6, 2024
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. Phys.-Math. Sci., Associate Prof., Belarusian State University, Minsk, 220030 Belarus, e-mail: dmitrukn@bsu.by
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Cite this article as: N.M. Dmitruk. A method for constructing multiply closed strategies in the problem of minimizing the total control impulse in a linear system with disturbance. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 3, pp. 122–138.
