The hybrid power system (HPS) is an emerging power generation scheme due to the plentiful availability of renewable energy sources. Renewable energy sources are characterized as highly intermittent in nature due to meteorological conditions, while the domestic load also behaves in a quite uncertain manner. In this scenario, to maintain the balance between generation and load, the development of an intelligent and adaptive control algorithm has preoccupied power engineers and researchers. This paper proposes a Hermite wavelet embedded NeuroFuzzy indirect adaptive MPPT (maximum power point tracking) control of photovoltaic (PV) systems to extract maximum power and a Hermite wavelet incorporated NeuroFuzzy indirect adaptive control of Solid Oxide Fuel Cells (SOFC) to obtain a swift response in a grid-connected hybrid power system. A comprehensive simulation testbed for a grid-connected hybrid power system (wind turbine, PV cells, SOFC, electrolyzer, battery storage system, supercapacitor (SC), micro-turbine (MT) and domestic load) is developed in Matlab/Simulink. The robustness and superiority of the proposed indirect adaptive control paradigm are evaluated through simulation results in a grid-connected hybrid power system testbed by comparison with a conventional PI (proportional and integral) control system. The simulation results verify the effectiveness of the proposed control paradigm.