A numerical method for solving linear-quadratic control problems with constraints

The paper is devoted to the optimal control problem for a linear system with integrally constrained control function. We study the problem of minimization of a linear terminal cost with terminal constraints given by a set of linear inequalities. For the solution of this problem we propose two-stage numerical algorithm, which is based on construction of the reachable set of the system. At the first stage we find a solution to finite-dimensional optimization problem with a linear objective function and linear and quadratic constraints. At the second stage we solve a standard linear-quadratic control problem, which admits a simple and effective solution.