On the modification of direct methods for solving optimal control problems of stationary thermal processes
Keywords:
stationary thermal process, control, system state, objective functional, gradient method, modified algorithm, efficiencyAbstract
Purpose. The aim of the study is to apply modified gradient-type methods to problems of optimal control of one-dimensional stationary thermal processes and to conduct a comparative analysis of the effectiveness of the classical and modified approaches using the example of solving specific problems. Design / Method / Approach. The research is focused on the development and numerical implementation of approximation-iteration algorithms based on the grid method for the analysis of controlled thermostatic systems modeled by differential equations with variable coefficients. For the numerical solution of the primary and adjoint boundary value problems, second-order accuracy difference schemes are used. To find the lower boundary of the objective functional, gradient-type minimization methods are used, both with and without control constraints. Findings. The proposed modified computational schemes demonstrate an increase in the efficiency of the classical grid method in terms of the amount of required computational costs and the accuracy of the obtained approximate solutions. Theoretical Implications. Expanding the possibilities of applying theoretically substantiated direct methods of accelerated convergence to solving optimal control problems of stationary thermal processes. Practical Implications. Creating an effective computational tool for solving optimal control problems of stationary thermal processes, which can be applied in practice. Originality / Value. Implementation of new computational schemes of accelerated convergence of modified gradient-type methods for the specified class of optimal control problems. Research Limitations / Future Research. The research limitations are due only to the properties of the programming language and software used. Further research involves applying the proposed modified approach to solving more complex optimal control problems, including multidimensional and phase-constrained ones. Article Type. Applied Research.
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