Abstract <p>A constructive technology for solving problems of dual-channel control of two heterogeneous systems that are interconnected by boundary conditions with distributed parameters in linear-quadratic optimization problems by the criterion of energy saving is proposed. The resulting spatial distribution of the controlled variables is approximated with the given uniform accuracy to the desired state. The developed technique initially employs a procedure of parameterization of the desired control actions on a finite-dimensional subset of an infinite number of final values of conjugate variables. The subsequent procedure is applied for the exact reduction to a parametric problem of semi-infinite optimization, which is solved according to the scheme of the previously proposed alternance method, which has been generalized to the studied situation. It is demonstrated that the equations of optimal controllers with lumped control actions for each of the objects are reduced to linear feedback algorithms on the measured state with nonstationary transfer coefficients. An illustrative example of optimization of the process of induction heating of two unbounded plates under conditions of ideal thermal contact on their boundary surfaces, which is of independent interest, is presented.</p>