Two-channel optimal energy-efficient control of distributed parameter systems

Abstract

A formulation and method for solving the problem of the energy-efficient two-channel programmed control of an object with distributed parameters with a given-precision uniform approximation of the resulting spatial distribution of the controlled quantity to the required state is proposed. Two internal controls on the power of heat sources in the electromagnetic field of the inductor are considered as control actions. Proposed solution approach involves a special-form preliminary parametrization procedure for control actions on finite-dimensional subsets of the terminal values of conjugate variables in the boundary-value problem of Pontryagin’s maximum principle, in combination with the subsequent reduction to a semi-infinite optimization problem, which is solved with respect to the requisite parameter vector using the alternance method based on additional information about fundamental laws of the subject area. An example of optimal energy-efficient control of transient heat conduction, which is of independent interest, is given.