Solution of the retrospective inverse heat conduction problem with parametric optimization

The retrospective inverse heat conduction problem has been solved as a problem of optimal control of an object with distributed parameters. The initial ill-posed statement of the inverse problem is transformed into a conditionally well-posed one when the limitations imposed on the second derivative of the desired control, which corresponds to a reduction of the set of control actions to the class of continuous and continuously differentiable functions, are taken into account. Preliminary parameterization of the control actions makes it possible to formulate a mathematical programming problem, which can be solved based on the analytical method of minimax optimization with alternance specific features of the desired optimal temperature deviations.