Optimization of Control with Anticipation and Delay for the Problem of the Shock Isolation of an Object on a Moving Base

The problem of protecting an object on a moving base from transient shock impacts (disturbances) using an active shock isolator is considered. The maximum displacement of the object relative to the base is selected as the minimized quality criterion. Based on the anticipating optimal control obtained for a disturbance in the form of an instantaneous impact, a guaranteeing control is constructed with optimization of the moment the control starting instant, which can be chosen with anticipation or with a delay. The proposed optimization is compared in terms of the performance index with the optimization with respect to the anticipation time only and with the case where both the anticipation time and the control starting instant are optimized.