OPTIMAL PROTECTION OF AN OBJECT ON A MOVING BASE FROM BOUNDED DISTURBANCES BY MEANS OF ANTICIPATING AND DELAYED CONTROLS

— The problem of constructing a guaranteeing control for a shock isolator that protects an object on a movable base from impacts to which the base is subjected is considered. The impact disturbance of the base is not known in advance and is modeled by the time history of the acceleration of the base. It is assumed that the impact acceleration is bounded, does not change in direction, and its duration and the integral over time are given. The control force is acting between the base and the object to be protected. This force is constrained in magnitude, and the absolute acceleration of the base can exceed the maximum absolute acceleration allowed for the body to be protected only on one time interval. The performance index to be minimized is the maximum displacement of the object relative to the base. A method is developed for determining within a specified class the worst disturbances that maximize the performance index. An effective control law that involves the optimization of the control starting instant is proposed on the basis of the combination of two control laws designed previously for the rectangular impact pulses and the disturbances with unbounded amplitude.