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Given a linear unknown system with $m$ inputs, $p$ outputs, $n$ dimensionalstate vector, and $q$ dimensional ecosystem, the problem of the adaptiveoptimal output regulation of this system boils down to iteratively solving aset of linear equations and each of these equations contains $\frac{n (n+1)}{2}+ (m+q)n$ unknown variables. In this paper, we refine the existing algorithm bydecoupling each of these linear equations into two lower-dimensional linearequations. The first one contains $nq$ unknown variables, and the second onecontains $\frac{n (n+1)}{2} + mn$ unknown variables. As a result, thesolvability conditions for these equations are also significantly weakened.

A Refined Algorithm for the Adaptive Optimal Output Regulation Problem