High order sliding mode control for restoration of a population of predators in a Lotka-Volterra system

Human-induced extinction and rapid ecological changes require the development of techniques that can help avoid extinction of endangered species. The most used strategy to avoid extinction is reintroduction of the endangered species, but only 31% of these attempts are successful and they require up to 15 years for their results to be evaluated. In this research, we propose a novel strategy that improves the chances of survival of endangered predators, like lynx, by controlling only the availability of prey. To simulate the prey-predator relationship we used a Lotka-Volterra model to analyze the effects of varying prey availability on the size of the predator population. We calculate the number of prey necessary to support the predator population using a high-order sliding mode control (HOSMC) that maintains the predator population at the desired level. In the wild, nature introduces significant and complex uncertainties that affect species' survival. This complexity suggests that HOSMC is a good choice of controller because it is robust to variability and does not require prior knowledge of system parameters. These parameters can also be time varying. The output measurement required by the HOSMC is the number of predators. It can be obtained using continuous monitoring of environmental DNA that measures the number of lynxes and prey in a specific geographic area. The controller efficiency in the presence of these parametric uncertainties was demonstrated with a numerical simulation, where random perturbations were forced in all four model parameters at each simulation step, and the controller provides the specific prey input that will maintain the predator population. The simulation demonstrates how HOSMC can increase and maintain an endangered population (lynx) in just 21-26 months by regulating the food supply (hares), with an acceptable maximal steady-state error of 3%.