From data to state model via energy Seminar

In a conservative system, all energy exchanged with the external world is stored. Storage means memory. And memory means state. Such considerations lead to a new approach to identification. I will illustrate the case of linear time-invariant and spatio-temporal systems, and of linear time-varying systems. I will show that by factorizing an “energy matrix” computed from external trajectories of the system, one can compute corresponding state trajectories.

To complete the identification of a state model, a system of linear equations must be solved. This identification procedure is analogous to subspace identification, where time-invariance is exploited. However, by making use of energy we can derive state equations also when time-invariance is absent (as in the case of time-varying systems) or it is cumbersome to take advantage of (as in the case of spatio-temporal systems).