New sweep algorithm for solving a continuous linear-quadratic optimization problem with unseptable boundary conditions

A new algorithm for solving the solution of the linear-quadratic optimization problem (LQP) with unseparated boundary conditions in the continuous case is given. Using the properties of symmetry of the corresponding Hamiltonian matrix, the Euler-Lagrange equations, it is shown that linear algebraic equations for determining the missing initial data of the system being solved have a symmetric principal matrix. The results are illustrated by the example of LQP optimization (stationary case) with minimal control actions.