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Context. The problem of the determination of the optimal value of the augmentation coefficient of a proportional governor includedinto an inertness-less linear object control system on the basis of a synthesized model is solved. The object of the presented study is theoptimal control process.Objective. The goal of the work is a creation of a method for a problematic situation of the optimum definition, evaluation, anddetermination solving at the control system.Method. A rough model of the phenomenon, and simplified dependence of optimal controlling trajectory upon the cost, of control inan inertness-less linear controlling system equipped with a proportional governor are proposed. The accuracy of the behavior of theinvestigated linear object of control has been chosen in the given consideration as an initial target value which needs to be minimized. The method of the model building with regards to an expenditures principle is offered. It provides taking into account the cost of controllingprocess. It allows finding the optimal controlling value on the multi-optional basis. There applied a certain analogue to the subjectiveentropy maximum principle of the subjective analysis in order to obtain a specific optimal distributions for the objective value in the viewof the composed functional. The method of the uncertainty degree of the options extremization is improved by a continuous optional valueintroduction that allows forming the value distribution density. The optional synthesized model of the control process is built.Results. The developed theoretical models allow obtaining, and have been implemented in, finding the hybrid optional density as anoptimal solution of a variational problem with two independent variables, which maximal value is the sought optimal controlling pathdelivering minimum to the integrated expenses pertaining with the process.Conclusions. The numerical experiments on the proposed methods studying in the problem of optimization are conducted. Thediscovered dependencies are substantiated as a result of these experiments. Their use in practice makes it possible, and is recommended, to carryout optimal control in the described systems. The prospects for further research may include creations of models for the optimal control trajectories findings on conditions involving rates of the considered values varying and in probabilistic, stochastic, undeterminedproblem settings.