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An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations
- Source :
- Games, Volume 12, Issue 1, Games, Vol 12, Iss 23, p 23 (2021)
- Publication Year :
- 2021
- Publisher :
- Multidisciplinary Digital Publishing Institute, 2021.
-
Abstract
- This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.
- Subjects :
- Statistics and Probability
Population
Bilinear interpolation
non-classic increment formulas
01 natural sciences
lcsh:Technology
lcsh:Social Sciences
0502 economics and business
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
ddc:330
Applied mathematics
050207 economics
0101 mathematics
education
Mathematics
education.field_of_study
lcsh:T
Applied Mathematics
010102 general mathematics
05 social sciences
Linear system
Function (mathematics)
Optimal control
hybrid systems
hyperbolic equations
lcsh:H
reduction of optimal control problems
Hybrid system
Ordinary differential equation
Statistics, Probability and Uncertainty
Hyperbolic partial differential equation
Subjects
Details
- Language :
- English
- ISSN :
- 20734336
- Database :
- OpenAIRE
- Journal :
- Games
- Accession number :
- edsair.doi.dedup.....9f78e322cb692c3b4e9322f7e14979fd
- Full Text :
- https://doi.org/10.3390/g12010023