Minimum energy capacity for “acceleration-braking” control

Basing on the generalization of the results for optimal controls designing of the "acceleration-deceleration" type of motion, whence the known special cases follow, universal analytical control function (translational acceleration) was found. Analytically and numerically was confirmed the existence of the limiting minimum control energy at which the movement of an object from the initial state of rest to a new state of rest is possible at a fixed distance and time of motion. Development of models and algorithms for optimal motion control of absolutely rigid and deformable bodies and systems is an urgent task. Basing on the reverse optimality principle (ROP), class of skew-symmetric controls for the translational and rotational motion of elastic systems with a finite and infinite number of degrees of freedom was found. The design of controls, taking into account the target of motion and restrictions, leads to the restoration of the functional criterion, which takes the minimum value during the movement.