| Abstract | dc.description.abstract | This paper deals with the control of discrete-time dynamical, monotone both in the state and in the
control, in the presence of state and control monotone constraints. A state x is said to belong to the
viability kernel if there exists a trajectory, of states and controls, starting from x and satisfying the
constraints. Under monotonicity assumptions, we present upper and lower estimates of the viability
kernel. Our motivation comes from harvest models, where some monospecies age class models, as well
as specific multi-species models (with so-called technical interactions), exhibit monotonicity properties
both in the state and in the control. In this context, constraints represent production and preservation
requirements to be satisfied for all time, which also possess monotonicity properties. Our results help
delineating domains where a viable management is possible. Numerical applications are given for two
Chilean fisheries. We obtain upper bounds for production which are interesting for managers in that they
only depend on the model’s parameters, and not on the current stocks. | es_CL |
