Analytical Conditions for Optimality in Inverse Problems of Heat Conduction

The solution of the inverse problem of technological physics is considered as a problem of the optimal control of an object with distributed parameters based on the Pontryagin maximum principle for an infinite-dimensional object formulated as necessary optimality conditions. The inverse problem of heat conduction is formulated in the uniform metric of estimation of the error in the description of the state function of the studied object and is reduced to the problem of the optimal control of an infinite-dimensional object with an integral quality functional and an extended state vector, for which the nature of the optimal control action is established with the Pontryagin maximum principle. The maximum principle method, which takes into account the relations that ensure that the solution belongs to a given compact set, makes it possible to obtain a parametric representation of the identified lumped or spatially distributed characteristics.