Some remarks on optimal output regulation for weakly dual redundant plants

In this paper the problem of optimizing the output regulation of a weakly dual redundant plant is addressed. When the system is under-actuated, only a subset of the outputs can be arbitrarily controlled, and the remaining ones are constrained. We investigate the problem of finding the input that minimize a cost function of the overall output tracking error, and how such solution is related to the inputs associated to the singularly optimal regulation of each output. Some interesting properties are revealed, such as the optimal solution being always included in the convex hull of singularly optimal controls and the existence of neutral reference spaces.