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[Enhancement] Output-feedback SLS_H2 function #5

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@TioMinho

Description

@TioMinho

Summary

The SLS_H2 function is already implementing the state-feedback SLS problem with $H_2$ norm. The output-feedback problem should now be implemented as a elseif case of the SLS_H2 function when the model is a GeneralizedPlant{<:Any,OutputFeedback}. This should be done using the ADMM-based implementation to separate the control and estimation sub-problems.

Proposal

  • Code the subproblems of the ADMM iterations. Ideally, they should be simply _SLS_H2(P, ___) and _SLS_H2(P',___) for the control and estimation problems, respectively.
  • Define the localization constraints $\mathcal{S}_x$ and $\mathcal{S}_u$ including the sparsity constraints for the $\Phi_{xy}$ and $\Phi_{uy}$ matrices.
  • Code the ADMM algorithm directly into the body of the SLS function (will be modular in future)
  • Boost performance by computing all the reduced-order systems prior to the ADMM loop.

Notes

  • The augmented Lagrangian function must be provided into a Distributed-friendly manner. Matrix operations should be preferred to avoid slicing and unnecessary allocations.
  • Should the number of iterations of the ADMM be a function argument, or stopping criteria is enough?

Implemented in: TBD

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