Optimal Output Regulation for Underactuated Systems with Quasiperiodic References

In this paper the problem of optimizing the output regulation of a weakly dual redundant plant is addressed. When the system is underactuated, only a subset of the outputs can be arbitrarily controlled, and the remaining ones are constrained. With a specific focus on quasiperiodic references, i.e. signals that can be written as trigonometric series, we investigate the problem of finding the input that minimizes the asymptotic output tracking error, and how such solution is related to the inputs associated to the singularly optimal regulation of each output.