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Received December 9, 2021; Accepted October 31, 2022; Published February 28, 2023
Abstract. This paper deals with an optimal control problem for a linear discrete-time system subject to input and state constraints and unknown bounded disturbances, where the control goal is to minimize a cost function used in linear explicit model predictive control. We define a solution to the problem under consideration in terms of optimal control strategies under the assumption that the state measurements of the system will become available at several future time instants (closing instants), the control loop at these instants will be closed and a new control input will be calculated. Such control strategies provide a compromise between a conservative optimal open-loop worst-case control and computationally demanding dynamic programming. A method for constructing optimal control strategies with one and multiple closing instants is proposed. The method reduces a multilevel optimization problem that arises from the definition of the control strategy to a number of linear programs resulting in low computational demands for the optimal strategy construction and its suitability for applications such as model predictive control, where the optimal control problem is solved online.
How to Cite this Article:
N.M. Dmitruk, D.A. Kastsiukevich, Optimal control strategies with multiple closing instants for linear systems with disturbances, Commun. Optim. Theory 2023 (2023) 9.