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628. Optimal control of one economic differential model of market relations
Invited abstract in session MA-33: Optimal control in supply chain management, stream Optimal Control Theory and Applications.
Monday, 8:30-10:00Room: 42 (building: 303A)
Authors (first author is the speaker)
| 1. | Phridon Dvalishvili
|
| Computer Science, Tbilisi State University | |
| 2. | Aleksandre Mosidze
|
| Mathematics And Computer Sciences, Free University Of Tbilisi | |
| 3. | Tamaz Tadumadze
|
| Tbilisi State University |
Abstract
For market relations, a controlled differential model with supply-demand functions and with delay parameter in control is constructed. We call the difference between supply and demand functions the disbalance index. It is assumed that consumer demand at any point in time will be satisfied through pre-ordering. To describe the development of the market equilibrium process over time, a dynamic model with an integral disbalance index is considered. For the proposed model an optimal control problem is studied. Namely, the existence theorem of an optimal control and the necessary conditions for optimality are formulated on the basis of results obtained in [1, 2]. In the case of a linear function of supply and demand, all controls that are doubtful of optimality are detected. An example is discussed at the end. Another case of optimal control of market relations was studied in [3].
References:
[1] Kharatishvili G. Tadumadze T. Formulas for the variation of a solution and optimal control problems for differential equations with retarded arguments. J. Math. Sci., 140 (1) (2007), 1-175.
[2] Tadumadze T. Variation formulas of solutions for functional differential equations with several constant delays and their applications in optimal control problems. Mem . Differ. Equ. Math . Phys., 70 (2017), 7-97.
[3] Dvalishvili Ph. Tadumadze T. Optimization of market relation model with delay. Journal of Modern Technology and Engineering 4(1) (2019) 5-10
Keywords
- Optimal Control
- Economic Modeling
- Control Theory
Status: accepted
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