Motivation
In the multi-model uncertainty set construction functionality of dkpy, the uncertainty weights must be constrained to be a diagonal matrix, a product of a scalar and identity matrix, or an identity matrix. These constraints are used in practice as they permit the use of SISO stable minimum-phase system fitting methods. However, they introduce conservatism in the multi-model uncertainty characterization.
Therefore, it would be useful to implement the computation of the optimal unstructured uncertainty weight frequency response and the overbounding fit of unstructured uncertainty weights.
Proposed Solution
Optimal Uncertainty Weight Frequency Response
Change the structure of the optimization variables in the current SDP implementation.
Uncertainty Weight Fit
Implement MIMO stable and minimum-phase spectral factor fit function.
- Pre-warp continuous-time frequency to discrete-time
- Fit discrete-time power spectrum to uncertainty weight frequency response
- Compute the discrete-time spectral factor of the power spectrum fit
- Convert the discrete-time spectral factor to continuous time
Additional Changes
- Update SISO stable minimum-phase system fitting methods
Motivation
In the multi-model uncertainty set construction functionality of
dkpy, the uncertainty weights must be constrained to be a diagonal matrix, a product of a scalar and identity matrix, or an identity matrix. These constraints are used in practice as they permit the use of SISO stable minimum-phase system fitting methods. However, they introduce conservatism in the multi-model uncertainty characterization.Therefore, it would be useful to implement the computation of the optimal unstructured uncertainty weight frequency response and the overbounding fit of unstructured uncertainty weights.
Proposed Solution
Optimal Uncertainty Weight Frequency Response
Change the structure of the optimization variables in the current SDP implementation.
Uncertainty Weight Fit
Implement MIMO stable and minimum-phase spectral factor fit function.
Additional Changes