This thesis presents advanced model-based concepts for the efficient loading control of a stratified storage tank. The loading is realized by means of a burner and a heat exchanger of the considered domestic heating system.As a prerequisite for the development and the application of model-based methods, the derivation of a rigorous plant model is outlined in a first step. The plant model, which is derived for the various operational modes of the heating system, comprises different combinations of partial and ordinary differential equations for the burner, the heat exchanger and the stratified storage tank.In a second step, model reduction techniques are used for the determination of reduced order simulation and design models. Thereby, the distributed parameter models of the heat exchanger and the burner are approximated by two different Galerkin approaches. The reduced-order model of the stratified storage tank is determined by use of a so-called high resolution slope limiter scheme.Based on these design models, state estimators are determined for the heating system. An early lumping Unscented Kalman filter and a late lumping distributed parameter observer are designed for the stratified storage tank. Luenberger observers are dimensioned for the heat exchanger and the burner.