2009/06/18 by Eladio Ocana Anaya, Michel De Lara, Anaya, Eladio Ocana +6
Decision Sciences · Engineering · Mathematics · #92D25 #92D40 #93B99 #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Simulation Techniques and Applications #Water resources management and optimization #math.OC #msc:92D25 #msc:92D40 #msc:93B99
paper · pdf · doi:10.48550/arxiv.0906.3506
arxiv created 2009/06/18 · openalex publication_date 2009/06/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider sustainable management issues formulated within the framework of control theory. The problem is one of controlling a discrete--time dynamical system (e.g. population model) in the presence of state and control constraints, representing conflicting economic and ecological issues for instance. The viability kernel is known to play a basic role for the analysis of such problems and the design of viable control feedbacks, but its computation is not an easy task in general. We study the viability of nonlinear generic ecosystem models under preservation and production constraints. Under simple conditions on the growth rates at the boundary constraints, we provide an explicit description of the viability kernel. A numerical illustration is given for the hake--anchovy couple in the Peruvian upwelling ecosystem.