Development of a method for the accelerated two-stage search for an optimal control trajectory in periodical processes

Optimization of manufacturing processes is the main tool that can provide access to the maximum financial efficiency of the enterprise. At the same time, this important tool for maximizing the resource efficiency is practically not used by enterprises due to the complexity and imperfection of the theory of optimal control, which manifests itself by its contradictory nature. The way out can be found by applying the method of practical determination of the optimal trajectory which was developed in the framework of this study. The advantage of the method is that it ensures determination of the optimal trajectory for those production processes which show intermediate results incomparable with each other both quantitatively and qualitatively. For example, to evaluate effectiveness of the operational processes associated with heating fluids, melting steel, crushing iron ore, etc. the costs and time alter nonlinearly at the intermediate stages. At the same time, qualitative parameters of the output product change which makes it impossible to use a direct method for estimating quantitative parameters of the output product at intermediate stages of the conversion process. The proposed method provides a two-stage process of optimization. In this case, completion of the first stage of optimization quickly transfers control to a zone close to the optimum in an automatic mode. The further search process just corrects the control trajectory if external conditions permit it. Thus, the proposed practical method of searching for the optimal control trajectory is essentially robust