A New Run Algorithm for Solving the Continuous Linear-Quadratic Optimal Control Problem with Unseparated Boundary Conditions

摘要

A sweep method is proposed for solving the optimal control problem with unseparated boundary conditions. This model reduces the boundary conditions to the initial condition. Using the properties of the J-symmetry of the corresponding Hamiltonian matrix and Euler- Lagrange equations, it is shown that linear algebraic equations for determining the missing initial data of the system being solved have a symmetric matrix of coefficients. The proposed algorithm allows us to reduce the dimension of the problem of finding the fundamental matrix of the Hamiltonian system. The results are illustrated by the example of a linear-quadratic optimal control problem (stationary case) with the minimal control actions.