Periodic tracking adaptive control for multivariable systems having more outputs than inputs

This note presents an adaptive control algorithm for multivariable systems in which the number of outputs is greater than the number of inputs. The algorithm can force the outputs to track arbitrary given reference signals periodically. This is the best tracking performance for systems lacking output function controllability. It has been shown that the tracking period is the upper bound on the controllability index of the controlled system. The proposed algorithm is applicable to multivariable systems with arbitrary interactor matrix but no knowledge of the interactor matrix is required.