Time-optimal control of the heating process with combined external influences by the boundary conditions

The formulation and method of solving the problem of optimal speed control of the heating process of an unlimited plate with two external influences on the boundary conditions, as one of which is considered the boundary concentrated control of the magnitude of the external heat flow, and the another is the heat flow, determined by a given ambient temperature. The solution of the problem is carried out under the conditions of a given accuracy of uniform approximation of the final temperature distribution over the plate thickness to the specified one. The method of finite integral transformations is used to find the input-output characteristics of an object with distributed parameters with two external boundary effects. The proposed method of solution of this problem is used the preliminary parametrization of control actions based on the analytical conditions of optimality in the form of the Pontryagin maximum principle and the subsequent reduction to the semi-infinite optimization problem, the solution of which is found using the alternance method. The alternance properties of the final resultant temperature state at the end of the optimal process leads to a basic system of relations, which, in the presence of additional information about the shape of the temperature distribution curve, is reduced to a system of equations that is resolved with respect to all the required unknowns. An example of solving the problem of optimal speed control of the temperature field of an unlimited plate with two boundary influences is presented.