  In this paper, we consider the problem of pollution control in a system that
undergoes regular regime shifts. We first show that the optimal policy of
pollution abatement is periodic as well, and is described by the unique hybrid
limit cycle. We next introduce the notion of an environmentally sustainable
solution, and demonstrate that such a policy is the only one that yields the
best possible trade-off between steadily achieving profit and ensuring
environmental preservation. In contrast to that, the policy that is not
environmentally sustainable eventually enters stagnation. To further illustrate
our findings, we compare the optimal periodic solution with a myopic one.
Interestingly enough, the myopic solution yields higher overall payoff in the
short-run, but completely fails in the long-run, while the environmentally
sustainable policy yields maximal payoff and preserves the environment over the
infinite time interval.
