Method of Quasi-Optimal Synthesis of Control Laws Based on the Reduction of the Lagrange Problem to the Isoperimetric Problem Using Asynchronous Variation

The solution of the problem of the structural synthesis of quasi-optimal control laws based on the reduction of the Lagrange problem to the isoperimetric problem is considered. The analysis of the variation of the extended action integral is based on the study of asynchronous (full) variation and leads to a boundary-value problem, the solution of which satisfies the condition for the maximum function of the generalized power and the requirement to fulfill the energy balance on the extreme trajectory. Based on the example of the problem of A.T. Fuller, it is shown that the set of quasi-optimal controls constructed using the developed method contains the optimal solutions.