Method of Integro-Differential Relations for Optimal Beam Control

An approach to modelling and optimization of controlled dynamical systems with distributed elastic and inertial parameters are considered. The general method of integro-differential relations (IDR) for solving a wide class of boundary value problems is developed and criteria of solution quality are proposed [1]. A numerical algorithm for discrete approximation of controlled motions is worked out [2] and applied to design the optimal control low steering an elastic system to the terminal position and minimizing the given objective function [3]. The polynomial control of plane motions of a homogeneous cantilever beam is investigated. The optimal control problem of beam transportation from the initial rest position to given terminal states, in which the full mechanical energy of the system reaches its minimal value, is considered. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)