MAINTENANCE OF AGE-STRUCTURED POPULATIONS: OPTIMAL CONTROL, STATE CONSTRAINTS, AND BANG–BANG REGIME
Natali Hritonenko, Yuri P. Yatsenko · Journal of Biological Systems · 2009
The paper analyzes the optimal maintenance of a "fully manageable" biological population with no natural reproduction. Examples of such populations include dairy farms, horse breeding, gardening, and forestry. Mathematically, the problem leads to the nonlinear optimal control of a first-order partial differential equation with pointwise state constraints. A necessary extremum condition is proven using the abstract optimization theory in Banach spaces. It is shown that the optimal dynamics has a bang–bang structure with three jumps and involves buying new young individuals and selling the old ones when their anticipated future expenses exceed the profit.