Optimization of Controlled Motions of a Linear Mechanical System

The motions of linear mechanical systems of a certain type are studied. The problem of designing a control that brings such a system to a given state in a fixed time and minimizes a functional, which is quadratic in the phase and control variables, is posed. The solution is sought within the framework of a generalized formulation of the problem with an integral representation of the system constitutive laws. A numerical optimization algorithm based on successive minimization of the constitutive and cost functionals is proposed. Approximation of the phase trajectory and input signals is constructed in the class of piecewise polynomial splines.