The article presents the statement of the problem, models and algorithms for controlling the welding process via robotic technological complexes in conditions of the risk of unstable states. The system dynamics model was used to describe the technological process. As system levels the basic indicators influencing quality of the made production chosen on the basis of experience of operation of the robotic technological complexes are taken. Functional dependences between indicators and their dependences on external factors are determined by approximation of statistical data. The procedure of identification of unstable states for the mathematical model on the example of the Rossler's attractor is developed. An algorithm for preventing the system from falling into unstable states in the process control is proposed.