Terminal controls synthesis method for the gibbs function use

Taking into account the physical features of the system as its invariants allows us to advance in solving the problem of the terminal controls structural synthesis. This is achieved through the Gibbs function use in the extended target functional formation. This determines the difference of the obtained result from the known ones. Application of the asynchronous variation method leads to the statement of the necessary condition for the targeted functional minimum. This is the basis for the equations of the boundary value problem within the Appell dynamical systems. Their final form is determined by the synthesis purpose. The expansion of these equations should be performed for specific cases. The reliability of the obtained results is confirmed by the terminal control problem solution. For linear systems, the proposed method allows one to obtain an exact analytical solution. The synthesized control ensures shock-free mode for change of the dynamic system state.