Adaptive robust optimal long-term management schemes for a class of ecological systems with partially known uncertainties

The problem of the optimal long-term management of uncertain ecological systems is considered. In this paper, the upper bound of the uncertainties of the exploited ecosystems is assumed to be unknown. An improved adaptation law with σ-modification is employed to estimate the unknown parameters, and a class of continuous adaptive robust state feedback control schemes is proposed. It is also shown that the proposed adaptive robust state feedback control schemes can guarantee the uniform asymptotic stability of the optimal steady state of exploited ecosystems in the presence of uncertainties. Finally, as a numerical example, an uncertain exploited ecosystem with two competing species is given to demonstrate the validity of the results obtained in the paper.