A nonlinear optimal control approach for the Lotka-Volterra dynamical system

Abstract

A nonlinear optimal (H-infinity) control method is developed for the Lotka-Volterra dynamical system. First, differential flatness properties are proven. The state-space description undergoes linearization, at each sampling instance, with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Next, for the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. Global stability properties are proven through Lyapunov analysis. Finally, the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.