On guaranteed control of the parabolic obstacle problem
Olga A. Nikishina - Master, Sr. Lecturer of Information and Communication Technologies Dept. M. Kozybayev North Kazakhstan University
Tatyana V. Pyatkova - Master, Sr. Lecturer of Information and Communication Technologies Dept. M. Kozybayev North Kazakhstan University
Abstract
The article deals with the study on the issue of guaranteed control of parabolic differential equations with constraints related to obstacles at the system level. The paper analyses methods for ensuring compliance with constraints when target states are achieved at a final point in time. The study pays particular attention to the utilisation of barrier functions, optimal strategies and stabilisation methods for the development of controls that guarantee the fulfilment of safety and efficiency conditions. The scientific novelty of the research lies in the development of a constructive algorithm for guaranteed control of a parabolic obstacle problem. The algorithm relies on adapting the model control method to a class of variational inequalities. The results obtained contribute to the development of the theory of controlling systems with constraints and have practical significance for modelling and controlling processes in thermophysics, the chemical industry, and biomedicine.
Keywords: guaranteed control; parabolic problem; obstacle problem; variational inequality; control with state constraints; free boundary.
For citation: Nikishina O. A., Pyatkova T. V. On guaranteed control of the parabolic obstacle problem. Digital Models and Solutions. 2025. Vol. 4, no. 4, pp. 59–68. DOI: 10.29141/2949- 477X-2025-4-4-5. EDN: NRALQZ.
