The Maximum Principle Applications of Time- Optimality for Linear Control Systems

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.