Integrodifferential Approach to Optimal Control Problems of Elastic Beam Motions
An approach to modeling and optimization of controlled dynamical systems with distributed elastic and inertial parameters is considered. The general method of integrodifferential relations (IDR) for solving a wide class of boundary value problems is developed and criteria of solution quality are proposed. A numerical algorithm for discrete approximation of controlled motions has been worked out and applied to design the optimal control lаw moving an elastic system to the terminal position and minimizing the given objective function. The polynomial control for 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 total mechanical energy of the system reaches its minimal value, is considered.