Abstract for: PID Control in a Toy Bio-economic Model

The mathematic control theory is applied to the development of modifications of the Schaefer fishery model. The key variables are the stock of the bio-resource, its natural net change, as well as the Man harvesting activity. The global and local analysis reveals quantitative and qualitative characteristics of closed loop control in a heuristic harvesting control rule in a two-dimensional model. Deeper analyses refine and generalize this rule in a three-dimensional model. The synthetic proportional, integral and derivative (PID) control together with parametric policy optimization maintains a robust harvesting control rule. Still unwarranted strength of integral control is destabilizing and can bring about Andronov – Hopf bifurcation in a local vicinity of a non-trivial stationary state. Key words: renewable resource, maximum sustainable yield, harvesting effort, PID control, optimization, Andronov – Hopf bifurcation