Natural Resource Management for Nonlinear Stochastic Biotic-Abiotic Ecosystems: Robust Reference Tracking Control Strategy Using Limited Set of Controllers

Abstract

The management of natural resources has become an important subject because of the increasing population. To meet human requirements for resources such as food and water, many control strategies have been proposed to improve biomass production and nutrient supply. However, implementing these strategies may be limited by the expense of large numbers of control devices and by the effects of stochastic perturbations. In this study, a robust reference tracking control strategy for the natural resource management of nonlinear stochastic biotic-abiotic ecosystems is proposed, using a limited set of controllers, to regulate the systematic dynamics achieving a desired reference trajectory under the influence of intrinsic fluctuations and environmental disturbances. To simplify the design procedure and make the robust reference tracking control strategy more feasible, we propose a fuzzy stochastic partial differrential equations system to represent the ecosystem, itself approximated by a fuzzy stochastic spatial state space model, based on a finite difference scheme. This allows replacement of a complex Hamilton-Jacobi integral inequality by an equivalent set of local linear matrix inequalities which can be easily solved. We verify the efficiency of the proposed approach using a nonlinear stochastic biomass-nutrient control example and compare the robust tracking control performance for different arrangements of control devices. Managers may select appropriate tracking control schemes based on this comparison. The robust reference tracking control strategy can be applied not only to agricultural systems but also to biophysical systems in ecological conservation, ecosystem restoration or engineering.

Keywords: natural resource management, spatial state space model, robust reference tracking control, T-S fuzzy interpolation, finite difference scheme