We study the problem of candidate control in participatory budgeting elections. Our focus is on two prominent sequential welfare-based rules---GreedyAV and GreedyCost---which are widely used in practice. Candidate control asks whether we can strategically modify the set of available candidates so as to either ensure that a preferred candidate $p$ is selected or prevent $p$ from being selected. Since all variants of candidate control under the two rules we consider are known to be NP-hard, we analyze the problems through the lens of parameterized complexity and approximability. Under the first lens, we provide a comprehensive classification with respect to natural parameters such as the number of voters, the number of controlled candidates, and the number of distinct costs, as well as their combinations. Within the second perspective, we establish a tight approximability bound.

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