Optimal boundary control for the nonlinear time-varying population system with diffusion

This article is concerned with the study of the optimal boundary control problem for the nonlinear time-varying population diffusion system with distributed observation. It proves the existence of the optimal boundary control, and obtains the necessary condition for the control and its optimality system. The optimal control is determined by the optimal system. An Euler-Lagrange system which is characterizing optimal control is also established. Then similarly some conclusions to the optimal control for the system with final state observation are obtained.