Abstract <p>This paper proposes a constructive method of solving the linear–quadratic problem of optimal control of hyperbolic systems with distributed parameters under the conditions of estimating in a uniform metric the target sets of final states of the controlled variable and the rate of its variation in time. The previously developed alternance method of constructing programmed control algorithms is applicable to the considered range of problems. The corresponding methodology uses the procedure of parameterization of the desired control actions on a finite-dimensional subset of an infinite number of final values of adjoint variables and the subsequent operation of exact reduction to a parametric problem of semi-infinite optimization, which is solved according to the scheme of application of the alternance method generalized to the situations under consideration. It is shown that the sought equations of the optimal controllers are reduced to linear feedback laws with time-varying coefficients based on the measurable output of the system. An example of the solution of the problem of the energy-optimal control of a system described by a wave equation of mathematical physics, which is of independent interest, is given.</p>