Fractional-order optimal control model for the equipment management optimization problem with preventive maintenance

The current quality status of most machinery and equipment is based on its accumulated historical status, but the influence of the past quality status on the current status of equipment is often overlooked in optimization management. This paper uses a Caputo-type fractional derivative to characterize this property. By refining the nature and characteristics of the equipment maintenance effect function and considering the memory characteristics of equipment quality, the existing model is improved, and a fractional-order optimal control model for equipment maintenance and replacement is constructed. Theoretical analyses verify the effectiveness of the fractional-order equipment maintenance management model. Furthermore, the results of numerical experiments also reflect this difference between integer-order and fractional-order equipment maintenance management models. The result shows that with an increase of the order alpha, the optimal target value of the equipment maintenance management problem will also increase with the weakening of the memory effect.