Pressure swing adsorption (PSA) assemblies with purge control systems, and hydrogen-generation assemblies and/or fuel cell systems containing the same. The PSA assemblies are operated according to a PSA cycle to produce a product hydrogen stream and a byproduct stream from a mixed gas stream. The byproduct stream may be delivered as a fuel stream to a heating assembly, which may heat the hydrogen-producing region that produces the mixed gas stream. The PSA assemblies may be adapted to regulate the flow of purge gas utilized therein, such as according to a predetermined, non-constant profile. In some embodiments, the flow- of purge gas is regulated to maintain the flow rate and/or fuel value of the byproduct stream at or within a determined range of a threshold value, and/or to regulate the flow of purge gas to limit the concentration of carbon monoxide in a heated exhaust stream produced from the byproduct stream.