ABSTRACT
The time-domainornorm-optimal algorithm is designed tominimize the quadratic optimizationproblem [1,8,10],
J = eTj+1Qej+1 + uTj+1Suj+1 + ( uj+1 − uj
)T R ( uj+1 − uj
) , (36.38)
where {Q, S,R} are symmetric positive (semi)-definite real-valued matrices of appropriate dimension and HTQH+ S is positive definite. Often {Q, S,R} ≡ {qI, sI, rI} with q, s, r real-valued positive scalars. Applying the substitution ej+1 = ej −H(uj+1 − uj), differentiating J with respect to uj+1, setting the result equal to zero, and rearranging the solution yields the norm-optimal ILC controller
uj+1 = Luuj + Leej, (36.39) Lu = (HTQH+ S+R)−1(HTQH+R), (36.40) Le = (HTQH+ S+R)−1HTQ. (36.41)
As an essential part of the design process, we discuss here some guidelines [16] for designing the weightingmatrices by studying the properties of the ILC systemwith respect to convergence, performance, robust convergence, and performance in the presence of trial-varying disturbances.
