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The paper deals with the determination of integral functional quality forcontrol system of generalized linear dynamic object with exponential activationfunction by solving the inverse problem of dynamic programming. The obtainedfunctionals contain two components that define the power consumption of thecontrol object and stability of the trajectories of control object. In somecases these components can not be represented by elementary functions but theirusing can improve accuracy and reduce the energy consumption of control object.

Design quality functionals for control systems with exponential activation function