Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 793512, 21 pages
Model-Matching-Based Control of the Beverton-Holt Equation in Ecology
Department of Electricity and Electronics, Faculty of Science and Technology, Institute of Research and Development of Processes, Campus of Leioa, Leioa Bilbao 48940, Spain
Received 24 July 2007; Revised 24 September 2007; Accepted 16 November 2007
Academic Editor: Juan Jose Nieto
Copyright © 2008 M. De La Sen and S. Alonso-Quesada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper discusses the generation of a carrying capacity of the environment so that the famous Beverton-Holt equation of Ecology has a prescribed solution. The way used to achieve the tracking objective is the design of a carrying capacity through a feedback law so that the prescribed reference sequence, which defines the suitable behavior, is achieved. The advantage that the inverse of the Beverton-Holt equation is a linear time-varying discrete dynamic system whose external input is the inverse of the environment carrying capacity is taken in mind. In the case when the intrinsic growth rate is not perfectly known, an adaptive law implying parametrical estimation is incorporated to the scheme so that the tracking property of the reference sequence becomes an asymptotic objective in the absence of additive disturbances. The main advantage of the proposal is that the population evolution might behave as a prescribed one either for all time or asymptotically, which defines the desired population evolution. The technique might be of interest in some industrial exploitation problems like, for instance, in aquaculture management.