Optimal control over a second-order dynamical system - Kopets, M.M. (Reports of the National Academy of Sciences of Ukraine, 2015)
The problem of minimization of the quadratic functional on solutions of the system of differential equations of the second order is considered. The method of Lagrange multipliers is applied to research the formulated optimization problem. Such approach has given a chance to obtain necessary conditions of optimality. On the basis of these conditions, the system of differential Riccati equations is deduced. The solution of this system permits us to write the closed formula for optimal control.