Varational approach and spline technique to optimization of controlled beam motions
An approach to modelling and optimization of controlled dynamical systems with distributed elastic and inertial parameters is considered. The general integrodifferential method for solving initial-boundary value problems is developed and criteria of solution quality are proposed. A numerical algorithm based on the variational approach for discrete approximations is worked out and applied to design optimal control moving an elastic system to terminal states and minimizing a given objective function. The optimal control problem of beam motion from the initial rest position to the terminal state, in which the total mechanical energy of the system reaches its minimal value, is considered.