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   Ludeke, Taylor; Iwasaki, Tetsuya (October 2024, IEEE Transactions on Automatic Control)

   A general problem encompassing output regulation and pattern generation can be formulated as the design of controllers to achieve convergence to a persistent trajectory within the zero dynamics on which an output vanishes. We develop an optimal control theory for such design by adding the requirement to minimize the H2 norm of a closed-loop transfer function. Within the framework of eigenstructure assignment, the optimal control is proven identical to the standard H2 control in form. However, the solution to the Riccati equation for the linear quadratic regulator is not stabilizing. Instead it partially stabilizes the closed-loop dynamics excluding the zero dynamics. The optimal control architecture is shown to have the feedback of the deviation from the subspace of the zero dynamics and the feedforward of the control input to remain in the subspace. 

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