A class of adaptive robust controllers with simpler structure and its application to uncertain ecological systems with time-delay

The problem of the optimal long-term management of uncertain time-delay ecosystems is considered. It is assumed that the upper bounds of the nonlinear delayed state perturbations are unknown and that the time-varying delays are any nonnegative continuous and bounded functions. In particular, it is only assumed that the nonlinear uncertainties, which can also include time-varying delays, are bounded in any nonnegative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain time-delay ecosystems, a new method is presented whereby a class of memoryless continuous adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the proposed adaptive robust state feedback control schemes can guarantee that the optimal steady state of exploited time-delay ecosystems can be uniformly exponentially convergent towards a ball which can be as small as desired. Finally, as a numerical example, an uncertain exploited ecosystem with two competing species is given to demonstrate the validity of the results.