Abstract: A multidimensional linear control object described by a vector differential equation is considered. The problem of programmed control with linear feedback is formulated in the presence of measurable and controlled external disturbing influences. To assess the quality of control processes, penalty (evaluation) functions are introduced, which are determined by the components of the control error vector. Based on the evaluation functions, criterion conditions are obtained, the fulfillment of which in a guaranteed way ensures the achievement of the goal of controlling the programmatic movement of the object. The obtained criteria conditions are used to form a system of algebraic equations with respect to the desired program control vector. The options for solving the obtained equations are considered.
Index terms: control object, programmed motion, disturbing influences.

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