Full analysis of the triple integrator problem

Consideration was given to the full analysis of the problem of optimal control using the method of synthesizing variables. The problem of control was formulated as that with fixed ends of the trajectory of the phase coordinate vector, fixed time interval, and bounded control. The plant dynamics was described by the model of the triple integrator, the functional being the power consumption. The results obtained can be used in the real-time design of power-saving control actions in the control systems of plants whose dynamics obeys differential equations of the third order.