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Synthesis of Controls for Nonlinear Multiply Connected Inertial Systems Using Variational Principles

The work is devoted to the synthesis of terminal controls by non-linear holonomic systems. The solution is based on the variational formulation of the problem in conjunction with the principle of the stationary Lagrange action for the Appell acceleration energy, which is used to form the extended functional by the method of uncertain Lagrange multipliers. An analysis of the variation of the extended functional leads to optimality conditions in the form of a two-point boundary value problem. A special example of its solution using the functions of A.N. Krylov. The synthesized control exactly coincides with the control of the Pontryagin maximum principle. This confirms the reliability of the results. It is shown that the decomposition of the initial system leads to n independent linear subsystems. This provides a solution to the problem of synthesis of terminal controls by non-linear holonomic systems. The effectiveness of the developed method is demonstrated by the results of mathematical modeling using the example of a two-link pendulum.