Optimal control and synchronization of Lotka–Volterra model

Abstract

In this paper we discuss the problem of optimal control for the steady state of Lotka–Volterra model. The conditions of the asymptotic stability of the steady state of this model are used to obtain the optimal control functions. In such study, the optimal Lyapunov function is used. The general solution of the equations of the perturbed state is obtained as a function of time. In addition, the optimal control is also applied to achieve the state synchronization of two identical Lotka–Volterra systems. Graphical and numerical simulation studies of the obtained results are presented.