Optimal Control of Unreliable Dynamic Systems with Discrete Time Inspections

The optimal control of unreliable dynamic systems where the mode (working or failed) is continuously inspected or monitored has received attention in the past. We consider the problem where instead of continuous inspection we have either no inspection or inspection at discrete time instants. The optimal feedback control is derived for the case where the system has no renewable capabilities. The case where a fixed number of renewals are allowed is briefly discussed.