Also known as Botrytis rot (Botrytis cinerea). The fungus that causes gray mold invades the plant and flower bracts that have been damaged by slugs ,frost, insects, or other factors. Infected plants turn brown on the outside. On the inner surface is the characteristic gray growth.
The fungus survives on decaying organic matter. Botrytis rot is most common during rainy weather. Plant in well-drained areas. Remove infected plant parts and protect plant buds from damage caused by invertebrates. When storing chokes, remove infected chokes immediately.
Fungicides registered for grey mold control must be applied before infection takes place, they won't cure an existing infestation. If you've had problems with gray mold in the past apply fungicide before the infestation gets to the plant.
Avoid injuring the foliage. Damaged foliage from Fertilizer-burn or frost- is much more susceptible to grey mold infection.
Avoid densely spaced seedlings growing levels by selecting a container that allows adequate spacing for seedling development.
Containers can also be placed at a wider spacing to allow better air circulation during periods when seedlings are especially vulnerable.
Fungicides effective against Gray Mold generally have Prothioconazole  as an active ingredient.
Artichoke Plume Moth
The larvae will feed on all parts of the plant, but their feeding on the buds and shoots is what causes the most damage. Larvae bore into the crown below the soil surface.
Beneficial Nematodes can keep the larvae stage in check.
Pesticides registered for use against the plume moth generally contain Esfenvalerate or an older version known as fenvalerate. They are sold under the trade names Conquer, Fenvastar, Shockwave, and Onslaught as well as several others.
Evergreen Pyrethrum Concentrate, a broad spectrum insecticide is also useful. It degrades quickly in sunlight so must be frequently re-applied. Active ingredient is pyrethrum, a Botanical Insecticide derived from a chrysanthemum flower.
Slugs and Snails
Slugs and snails are a major problem on perennial artichokes especially in winter. They feed on all parts of the plant. Slug feeding on foliage causes shot holes on the leaves. Slugs are particularly injurious to the buds when they scrape off soft tissues from the artichoke bracts. This injury later turns black and the quality of the affected produce is greatly reduced. See Controlling Controlling Snails and Slugs.
Cutworms are larvae of of a large family of dull-colored , night-flying moths, often visible around lights in Spring, They come in various colors, but are generally a dull gray and well camouflaged within the soil. They are soft-bodied, hairless caterpillars that curl up when touched. Fully grown, they are less than 2 inches long.
Cutworm larvae chew young plants off at the base at or near ground level. When you see a freshly severed plant, carefully stir the soil around it and you can usually find and destroy the culprit before it can move to the next plant.
Footnotes - References
[1.] Prothioconazole Pesticide Fact Sheet - EPA - National Service Center for Environmental Publications.