Методы и модели в экономике
Динамические системы
Valery N. Afanas’ev, Nataly A. Frolova Differential game in the problem of controlling a nonlinear object with restrictions on control actions
Applied aspects in informatics
Системный анализ в медицине
Valery N. Afanas’ev, Nataly A. Frolova Differential game in the problem of controlling a nonlinear object with restrictions on control actions

The optimal control problem in the differential game problem with restrictions on the control actions for a class of controlled dynamic systems whose nonlinear objects which can be represented as objects with a linear structure and state-dependent parameters (SDC-model) is formulated. The linearity of the structure of the transformed nonlinear system and the quadratic functional quality of a special kind allow for the synthesis of optimal control, i.e. finding the parameters of the controller, go from the need to search for solutions of the Bellman-Isaacs equation to the equation of Riccati type with state-dependent parameters. The synthesized controls provide the SDC-model with the property of asymptotic stability and allow one to determine the ratio of constraints imposed on the controls under which the condition for the existence of a differential game with zero sum. As an illustration of the results obtained, a simulation of the behavior of a nonlinear system with two players on an infinite control interval (with an open horizon) is given.


extended linearization method, non-classical functional, Bellman-Isaacs equation, Riccati equation with state-dependent parameters.

DOI: 10.14357/20790279200307

PP. 56-64.

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