Modeling and Optimization of Elastic System Motions by the Method of Integro-Differential Relations

摘要

We explore the possibility of constructing a solution satisfying prescribed performance criteria and the possibility of optimizing the motions of elastic systems with distributed parameters. The regular integro-differ-ential approach of [1] to the construction of solutions for a wide class of boundary value problems is developed, and a performance criterion for the resulting solutions is proposed. A polynomial control is applied to the plane motions of a homogeneous rectilinear elastic beam. An algorithm is developed for constructing an optimal control that drives the system to a terminal state with the minimal total energy at a given time. The results obtained by the method of integro-differential relations are analyzed.