Control theoretic models of environment-economy interactions

A class of infinite-horizon optimal control models is described that link economic growth and pollution control models by coupling the standard investment-consumption equations to a pollution control equation. A distributed parameter model taking into account spatial distributions of capital and pollution is emphasized. The performance of the system is measured by an integral cost functional which, for T >0, measures the total net benefit or utility accumulated over the time interval [0,T]. The goal is to maximize this utility over the time interval [0,+∞]. The authors consider an undiscounted utility to avoid weighting the decisions to the present at the expense of the future. This consideration leads to a divergent objective functional which requires one to consider the overtaking optimality concept. Conditions under which there exists an overtaking optimal solution and an associated steady state which attracts the optimal trajectory are provided. Thus, an acceptable level of pollution is arrived at