Faus i dont have reference with acrylic acid and amines Michael addition but believe me it works
Theres many references on using different catalists for these reactions and may be interesting for you can be this:
"LiClO4 Accelerated Michael addition of amines to ?,?-unsaturated olefins under solvent-free conditions" N. Azizi, M. R. Saidi, Tetrahedron, 2004, 60, 383-387.
Insted of acrylic acid you may use acrylonitrile CH2CHCN which has low boiling point than acrylic acid and easier removed the excess from the reaction mixture but then you should think how best to hydrolize the nitrile group of obtain derivate to carboxylic group without hydrolize the other ethyl ester group so may be better first suggested from me reaction directly with acrylic acid...
For the first step in synthesis of ethyl amino crotonate with NaNH2 be careful with this reagent and think if theres other efficient reactions for obtainig desired amine.
Think also about possible routes from crotonate amine with 3-bromo propanic acid for N-alkylation or with NHMgX salt(from amine + MeMgI Grignard- first should react quantitly the amine with methyl grignard before possible side reaction with the ester group if use excess Grignard reagent) with the 3-bromo propanic acid.
Regards