Abstract <p>This article presents an analysis of approaches and methods for determining the processing mode (mechanical, local thermal, welding, thermal cutting, etc.). It is shown that the problem of determining the processing mode is inverse in its formulation, characterized by a violation of the cause-and-effect relationship inherent in a real thermal process. More effective methods for solving inverse problems are the methods and principles of optimal control theory. The first problems of optimal control of thermal processes of material processing by concentrated energy flows were set and solved in 1976 at the Baikov Institute of Metallurgy and Materials Science of the USSR Academy of Sciences as one-dimensional problems of thermal conductivity. Two- and three-dimensional problems of optimal control were set later and solved using the same methods of the theory of optimal control of systems with distributed parameters. The use of optimal control principles and the capabilities of modern computing technology make it possible to reduce the number of full-scale experiments when determining the processing mode and increase the efficiency of technological processes being developed.</p>