Optimal Work-Rest Cycles

Assuming an instantaneous benefit proportional to a system's state we determine the optimal work-rest policy so as to maximize the average cycle benefit, provided the state declines exponentially when the system is active and increases exponentially when it is at rest. Any given lower bound for the length of a rest period determines a unique optimal limit cycle, towards which an optimal state trajectory converges, irrespective of its starting point. The cycle benefit is maximal when the length of the resting period converges to zero while the work-rest split remains nontrivial. For this limiting case, we provide a relatively robust estimate of the system’s unknown time constants.