Projective synchronization of the generalized Lotka-Volterra system with asymptotically unbounded external disturbance

Abstract

This paper investigates the projective synchronization problem of the generalized Lotka-Volterra (GLV) system in the presence of unbounded external disturbance. Firstly, a unified projective synchronization control law is proposed for the nominal GLV system, which verified the existence of the projective synchronization problem. Secondly, a suitable filter is designed to estimate the asymptotically unbounded external disturbance that is incorporated into GLV system, by which a simple yet general disturbance estimator-based control strategy is derived to achieve the asymptotically stable of the error system. Finally, numerical simulations are performed to demonstrate the correctness and validity of the theoretical results.

Stabilization of the GLV System with Asymptotically Unbounded External Disturbances

“…This leads to the fact that the proposed results are too conservative in some cases. In recent years, the DE-based method [15] has been shown to be an improvement of the UDE-based method; it has shown some advantages in handling some asymptotically unbounded external disturbances. But, for some asymptotically unbounded external disturbances, such as (A 2 t 2 + A 1 t + A 0 )e at , where A 0 , A 1 , A 2 are unknown constants, whereas a is a small known constant, there is still a lack of effective handling methods, even for the feedback based on deep reinforcement learning [16][17][18].…”