Control of elastic systems by bounded distributed forces

摘要

Linear elastic systems controlled by distributed bounded forces are considered. We propose a method of control that brings the system to the prescribed terminal state in a finite time. The approach is based on a decomposition of the system into an infinite number of subsystems with one degree of freedom each. After that, we apply the time-optimal control to each mode. As a result, explicit formulas for control forces are obtained. Estimates on the duration of the control process are given. As examples, we present sufficient controllability conditions for elastic membranes and beams.