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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 finitedimensional optimization problem with a linear objectivedoi:10.15826/umj.2016.2.009 fatcat:gr72ssh5jzg4dcg4t6nbgqqgm4