Abstract:
Mathematical control theory is a branch of mathematics having as one
of its main aims the establishment of a sound mathematical foundation for the
control techniques employed in several different fields of applications,
including engineering, economy, biology and so forth. The systems arising from
these applied sciences are modeled using different types of mathematical
formalism, primarily involving ordinary differential equations, or partial
differential equations or functional differential equations. Optimal control
theory-which is playing an increasingly important role in the design of modern
systems-has as its objective the maximization or the minimization. In this
research we consider a mathematical model of mosquito and insecticide, fish
harvesting.The aim of these models is first, reduce the amount of mosquitoes in
the ponds and swamps because Mosquitos are the main cause of malaria
disease.We used the optimal spray strategies to minimize amount of mosquito.
Second increase the profit to the maximum extent of the harvest during a
specific time period. We used the strategies optimal control to maximize the
profit of fish harvesting. We work optimal control framework by applying the
Pontryagin's maximum principle. A characterization of the optimal control via
adjoint variables was established. We obtained an optimality system that we
sought to solve numerically by used MATLAB program.
