Theoretical Interpretation for Some Relationships in H∞ Setting

摘要

The paper discusses relationships between the H∞ preview control and the standard H∞ control, between the H∞ fixed-lag smoothing and the H∞ filtering. It is easy to understand intuitively that the H∞ preview control problem is inevitably solvable if the standard H∞ control problem for the identical system is solvable and that the H∞ fixed-lag smoothing problem is solvable as the H∞ filtering problem is solvable for the same system and measurements. However, the theoretical interpretations for these two phenomenons so far have not been found in any existing literatures. Hence, the paper makes use of Innovation Re-organization analysis to derive and provide a rigorous and theoretical interpretation for the relationships, which are very similar to the relationship between the H2 smoothing and the H2 filtering.