Some features of the problems of computational optimization in the computer-integrated systems

Fìz.-mat. model. ìnf. tehnol. 2021, 32:64-69

Abstract

For quality control in computer-integrated systems, it is assumed that the calculation of control signals is based on mathematical models of control objects. When solving the equations of the dynamics of the control object, it is necessary to take into account the limited computing resources of computer-integrated systems, which requires the choice of an effective method of solving equations, provided that the required accuracy of calculations. The paper considers a method for solving computational optimization problems in computer-integrated systems based on the proposed optimality criteria. A method is proposed based on the estimation of the discrepancy between the obtained and the reference solution to estimate the global error. The solution is accepted, the accuracy of which is two orders of magnitude higher than the required modeling accuracy.

References

1. Sergiyenko, I. V., Zadiraka, V. K., Babych, M. D. (2006). Computer Technology for Solving Problems Applied and Computational Mathematics with Predetermined Values Quality Characteristics. Суbernetics and Systems Analysis, 42(5), 33-41.
2. Verlan, A. A., Mytko, L. A., Dyachuk, A. A., Fedorchuk, V. A. (2007). On the choice of numerical methods for solving differential equations for modelling and control systems. Modelling and information technology. Collection of scientific works G. E. Pukhov Institute for Modelling in Energy Engineering NAS of Ukraine, 44, 90-95.
3. Verlan, A. A. (2017). Method of construction of specialized algorithms for solving differential equations. Mathematical and computer modelling. Series: Technical sciences. V. M. Glushkov Institute of Cybernetics of the NAS of Ukraine, K-PNU. Kamianets-Podilskyi: K-PNU, 16, 30-35.
4. Khimich, A. N., Popov, A. V., Chistyakov, O. V. (2017). Hybrid algorithms for solving the algebraic eigenvalue problem with sparse matrix. Суbernetics and Systems Analysis, 53, 132-146.
   DOI doi.org/10.1007/s10559-017-9996-5
5. Verlan, A., Fedorchuk, V. (2017). On the choice of numerical methods for solving dynamic equations for control systems with embedded calculating tools. Mathematical and computer modelling. Series: Technical sciences. V. M. Glushkov Institute of Cybernetics of the NAS of Ukraine, K-PNU. Kamianets-Podilskyi: K-PNU, 15, 37-44.