Photopolymerization-based Additive Manufacturing (AM), a technique in which a product is built in a layerwise fashion by local curing of a liquid monomer, is increasingly being adopted by the high-tech sector. Nevertheless, industry still faces several challenges to improve the repeatability of product quality, as recognized by several authorities on AM standardization. It is commonly recognized that there is a need for an in-depth understanding, in-situ monitoring and real-time control of the curing process to work towards end-products of higher quality. This motivates the investigation on closed-loop control of the curing process and the build-up of material properties. This pioneering research contributes to the development of a control-oriented model in the form of a state-space description that describes the multiphysical photopolymerization process and connects curing kinetics, heat flow, strain and stress evolution. This work focuses on one spatial dimension and is extendable to higher dimensions. Moreover, an extension to existing control systems theory is proposed to anticipatively control the process through the quadratic tracking framework. The control strategy is based on sequential linearization of the nonlinear model obtained from multiphysical modelling. This theoretical-numerical approach demonstrates the potential of model-based control of the material property build-up during vat photopolymerization processes such as stereolithography and serves as a proof of principle.