But similar to the considerations in Section 2, we could start from an initial parameter error covariance matrix K 0 that is not circulant, e.g., K 0=w w T. In this case, K 0 can be separated in one part that lies in the modal space, defined by F, and one part from its complement space.
Possible worlds are points in modal space as defined by the modal axes just as physical spatiotemporal points are points in physical spacetime as defined by the four physical spatiotemporal axes, and possible objects "persist" through possible worlds.
A linear transformation is established between the two modal spaces spanned by the modes, respectively, for the reinforced and the unloaded plates.
Then, any initial parameter error covariance matrix K 0 evolves only in the modal space of R uu, now defined by DFT matrices F∈IC M×M.
Particularly interesting is the fact that the parameter error covariance matrix is essentially being forced to remain in the modal space of the driving process, defined by its autocorrelation matrix R uu.
The control problem is solved by using the independent modal space control technique.
The concept of independent modal space control is adopted, and the system is studied by the discrete-time model.
The modal approach further modifies the probabilistic approach by defining semantic information in terms of modal space and in/consistency.
Then, based on the proposed dynamics model, by constructing the modal filter, a robust H∞ independent modal space controller is designed and utilized to decouple the piezo-stage and deal with the unmodeled dynamics, disturbance, and hysteresis compensation error.
