Control of uncertain discrete systems: an application in resource management

The authors consider the problem of stabilizing the management of uncertain fishery resources. The stabilization of management policies is connected with the design of memoryless state-feedback control strategies for a class of discrete-time resource models which contain unknown but bounded fluctuations. The theory is based on conditions developed for a Lyapunov-type stability of sets. The theory is illustrated by simulation examples from fishery economics. Parent stock is stabilized by a feedback harvesting strategy when the catchability of the resource or the stock-recruitment relationship fluctuates. Entry and exit of fishermen are stabilized in an open-access common-property fishery, where the entry and exit dynamics are determined by fluctuating revenues obtained from the fishery