Desired Behavior
The current multi-model uncertainty characterization computes optimal uncertainty weight frequency responses by minimizing the trace of uncertainty weight power spectrum. However, this does not directly minimize the measure, or volume of the uncertainty set at a given frequency as the measure is related to the determinant of the weights.
Therefore, a multi-model uncertainty characterization method should be implemented that directly minimizes the measure of the uncertainty set at a given frequency.
Proposed Solution
An optimization problem can be posed that maximizes the log determinant of the inverse of the uncertainty weights (which minimizes the measure of the uncertainty set). Moreover, BMI constraints can be constructed in terms of the relevant design variables to enforce that the uncertainty model covers all off-nominal responses.
Desired Behavior
The current multi-model uncertainty characterization computes optimal uncertainty weight frequency responses by minimizing the trace of uncertainty weight power spectrum. However, this does not directly minimize the measure, or volume of the uncertainty set at a given frequency as the measure is related to the determinant of the weights.
Therefore, a multi-model uncertainty characterization method should be implemented that directly minimizes the measure of the uncertainty set at a given frequency.
Proposed Solution
An optimization problem can be posed that maximizes the log determinant of the inverse of the uncertainty weights (which minimizes the measure of the uncertainty set). Moreover, BMI constraints can be constructed in terms of the relevant design variables to enforce that the uncertainty model covers all off-nominal responses.