A computational approach to optimization of controlled mechanical systems

In the present work we consider a class of nonlinear optimal control problems, which can be called "optimal control problems in mechanics". We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem we propose an implementable numerical algorithm.