Dual-channel control with minimum energy consumption in linear-quadratic optimization problems of interconnected heterogeneous systems with distributed parameters

A constructive technology for solving problems of dual-channel control of two heterogeneous systems 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 controlled variables is approximated with 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. Subsequent procedure is applied for 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 situation under study. 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 non-stationary 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 is presented, which is of independent interest.