Erratum: “Frequency Domain Adjoint-Based Iterative Learning Control for MIMO Systems” [ASME Letters Dyn. Sys. Control, 2025, 5(2), p. 021007; DOI: 10.1115/1.4067535]

Abstract

An operation error occurred in the equations of the final publication, please find the corrected equations as follows: Equation (4) should be written as J(u)=12eTe.Equation (6) should be written as ∇J(uk)=GTek.Equation (8) should be written asGT=[(G11)T…(Gno1)T⋮⋮(G1ni)T…(Gnoni)T]=[T0⋱0T]⏟Tni[G11…Gno1⋮⋱⋮G1ni…Gnoni]⏟G~[T0⋱0T]⏟TnoThe paragraph under Eq. (8), both GkG should be written as GTek.Equation (9) should be written asuk+1=uk+ρGTek=(IniN−ρGTG)uk+ρGTydesThe paragraph under Eq. (9) should be corrected as “where IniN is an identity matrix of size niN×niN.”Equation (10) should be written as ρ*=1‖GTG‖=1‖G‖2In the sentence right after Eq. (10), ‖Gke‖2 should be written as ‖GTek‖2Equation (11) should be written asρ*=1maxω‖G(ejω)‖2≈‖ek‖2‖GTek‖2,