The problem of synthesis of the optimal controls using nonlinear dynamic systems in general form is not yet analytically solved. Fundamental results of L.S. Pontryagin leads to programs of optimal control, and the solution to the synthesis problem can be obtained using complex constructions only in special cases. The implementation of such solutions implies the need to take into account the sliding modes, the regimes of frequent switching, the negative influence of interference, and so on. This was the reason for the development of methods for synthesizing systems of variable structure, which allow to increase the accuracy of control, eliminate undesirable modes, and counteract the influence of external and parametric disturbances. The results of the research showed that using the combined maximum principle leads to obtaining a general structure of quasi-optimal control for different classes of constraints and allows to provide parametric and structural adaptation to of the state and the parameters due to the possibility of complex implementation of control principles with respect to deviation and disturbance.
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