
Valery N. Afanas’ev, Nataly A. Frolova Differential game in the problem of controlling a nonlinear object with restrictions on control actions 

Abstract.
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 statedependent parameters (SDCmodel) 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 BellmanIsaacs equation to the equation of Riccati type with statedependent parameters. The synthesized controls provide the SDCmodel 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.
Keywords:
extended linearization method, nonclassical functional, BellmanIsaacs equation, Riccati equation with statedependent parameters.
DOI: 10.14357/20790279200307
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