Global stabilization of the planar Ricker system with noisy PBC

TL;DR

This paper develops a control method using Prediction-Based Control to globally stabilize the positive equilibrium of a noisy planar Ricker system, ensuring stability through Lyapunov functions and stochastic parameter perturbations.

Contribution

It introduces a novel control approach combining PBC with stochastic parameter adjustments for global stabilization of the Ricker system.

Findings

Successful stabilization demonstrated via computer simulations.

Derived conditions on control parameters for stability.

Effective reduction of control effort through stochastic perturbations.

Abstract

We apply Prediction-Based control (PBC) in order to stabilize globally a positive equilibrium of a planar Ricker's equation. We construct a closed invariant set in a strictly positive domain for the controlled map and derive conditions on control parameters ensuring that the increments of a specially constructed Lyapunov function are nonpositive on this set. By stochastic perturbation of the parameters we decrease the average values of controls providing global, as well as local, stabilization. Computer simulations illustrate our results.