New control algorithms are required to deal with the intermittent, stochastic, and distributed nature of the generation and new consumption patterns. Control of micro-grids poses significant challenges that need to be addressed through advanced control techniques. This paper investigates an optimal control strategy that efficiently manages a stand-alone residential micro-grid comprising renewable and non-renewable energy sources. An adaptive model predictive control (AMPC) algorithm is implemented for choosing an optimal mode and set of inputs for the system to track both a constant and load-varying power demand profile. The problem to be solved by the AMPC control algorithm is to perform an optimal power reference tracking problem, where the consumption of energy from the diesel generator is minimized while maximizing the efficiency of the storage bank. The objective of the optimal control scheme is for the generation to meet the demand, minimize the use of fossil fuels and ensure the energy storage is always maintained around a nominal point such that it is not over-depleted. Therefore, the main goal is to maximize the use of renewable sources and minimize traditional sources. The design and simulation of the plant model and the AMPC controller are carried out on the MATLAB/Simulink environment.