Optimizing output regulation for a class of underactuated LPV systems

In this paper the problem of optimizing the output regulation of an underactuated LPV system is considered. When the system is underactuated, only a subset of the outputs can be arbitrarily controlled, and the remaining ones are constrained. The problem of finding the input that minimizes a cost function of the overall output tracking error is investigated for a special class of LPV systems that admit steady-states. Moreover, it is shown how such solution is related to the inputs associated to the singularly optimal regulation of each output.