Context. Various studies have emphasised variations in the charge state and composition of the interstellar polycyclic aromatic hydrocarbon (PAH) population in photodissociation regions (PDRs). These changes are expected to affect the energetics and chemistry in these regions, thereby calling for a quantitative description. Aims. We aim to model the spatial evolution of the charge and hydrogenation states of PAHs in PDRs. We focus on the specific case of the north-west (NW) PDR of NGC 7023, for which many observational constraints are available. We also discuss the case of the diffuse interstellar medium (ISM). Methods. We modelled the physical conditions in NGC 7023 NW using a state-of-the-art PDR code. We then used a new PAH chemical evolution model that includes recent experimental data on PAHs and describes multiphoton events. We considered a family of compact PAHs bearing up to 96 carbon atoms. Results. The calculated ionization ratio is in good agreement with the observed ratio in NGC 7023 NW. Within the PDR, PAHs evolve into three major populations. We find medium-sized PAHs (50 N C 90) to be normally hydrogenated, while larger PAHs (N C 90) can be superhydrogenated, and smaller species (N C 50) are fully dehydrogenated. In the more diffuse gas of the cavity, where the fullerene C 60 has recently been detected, all the studied PAHs are found to be quickly fully dehydrogenated. PAH chemical evolution exhibits a complex non-linear behaviour as a function of the UV radiation field because of multiphoton events. Steady state for hydrogenation is reached on timescales ranging from less than a year for small PAHs, up to 10 4 years for large PAHs at A V = 1. Critical reactions that would need more studies are the recombination of cations with electrons, the reactivity of cations with H 2 , and the reactivity of neutral PAHs with H. Conclusions. We have developed a new model of PAH chemical evolution based on the most recent available molecular data. This model allows us to rationalise the observational constraints without any fitting parameter. PAHs smaller than 50 carbon atoms are not expected to survive in the NGC 7023 NW PDR. A similar conclusion is obtained for the diffuse ISM. Carbon clusters turn out to be end products of PAH photodissociation, and the evolution of these clusters needs to be investigated further to evaluate their impact on the chemical and physical evolution of PDRs.