Impulse controls in optimal harvesting of age-structured populations

A nonlinear optimal control problem in the Lotka–McKendrick population model is studied. It describes rational management of age-structured farmed populations in aquaculture and indoor farms. Employing generalized functions, we prove the impulse nature of optimal harvesting. Exact analytic solutions for sustainable harvesting strategies are obtained and used to analyze the optimal dynamics of harvesting age and rotation under technological innovations.