Primal-dual method for solving a linear-quadratic multi-input optimal control problem

In this paper, we intend to minimize a quadratic terminal functional on the trajectories of a linear dynamic system. The algorithm of optimization is constructed on the basis of support methods of linear and quadratic programming and their applications in the constructive theory of optimal control. Here we develop a constructive primal-dual method for the case where the control is a multivariable function. The algorithm is illustrated on two numerical examples in mechanics.