In the theory of optimal control, the attainable set of controlled objects $D(T)$ at moment $T$ plays an important role. For example, this set is useful in studying the dynamical possibilities of controlled objects. We study the character of dependence of the attainable set of linear controlled objects on disturbances of its dynamical characteristics. This paper establishes several sufficient conditions that guarantee such a property: if the dynamical characteristics of the controlled object change little (in a certain sense), then the attainable set changes little in the Hausdorff metric.
Keywords: linear controlled object, measured control, attainable set, Hausdorff metric
Received February 4, 2025
Revised March 7, 2025
Accepted March 10, 2025
Mikhail Sergeevich Nikol’skii, Dr. Phys.-Math. Sci., Prof., Steklov Mathematical Institute of the Russian Academy of Science, Moscow, 119991 Russia, e-mail: mni@mi-ras.ru
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Cite this article as: M.S. Nikol’skii, On the dependence of the attainable set of linear controlled objects on disturbances. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 2, pp. 155–161.
