The efficient exploitation of production inventory systems is of significant importance in the modern industrial reality. This paper explores the effect of such a system on dynamic behaviour of a system when the control is provided synergistically by a method called synergetic control (SC). The mathematical model of the system is first constructed and SC introduced to improve the responsiveness of the system when the time-varying demand condition is taken into account. To cope with the problem of unavailability of the systems' state signals and to estimate the demand, the extended state observer (ESO) is introduced. Moreover, mountain gazelle optimizer (MGO) is employed to tune the adjustable design parameters of the SC and the ESO based on the integral of absolute error (IAE). The enhanced ability of the extended state observer (ESO) to provide an estimate of the system states and profiles of the demand can be verified by numerical simulations utilizing in MATLAB software. Moreover, the performance of the proposed ESO-SC is compared with the proportional-integral-derivative (PID) controller. These results demonstrate that the ESOSC achieves superior performance enhancement, particularly through a significant reduction in inventory costs.
