Regulation of fishery: from a local optimal control problem to an "invariant domain" approach

This study aims at regulating a fishery by reducing its catch and effort variations around a reference equilibrium point. A simple bioeconomic continuous time model is considered and the control variable acts on the rate of change of effort. Two approaches have been implemented: the first one is a local optimal approach that sets the problem in the classical linear-quadratic framework; it is extended to an "invariant domain' approach, whose robustness constitutes a major advantage.