Optimally controlled steady-states for multi-input underactuated linear systems

In this paper the problem of optimizing the regulation of a weakly dual redundant plant with multiple actuators is addressed. When the system is underactuated, only a subset of the outputs can be independently controlled. In this regard, the main objective of the paper pertains the optimization of the steady-state performance of the plant. A connection between the overall optimal input and the inputs that provide a perfect reference tracking of the full controllable square subsystems is established. The proposed control scheme is validated by the simulation experiment of a tracking problem for a three mass coupled system.