Abstract
This paper, first, presents that the optimal preview control system (named OPCS) with preview actions over a fixed control inteval is equivalent to the least-squares smoother (named LSS) in the limit where x(0) and X0 tend to zeros, where x(0) and X0 respectively denote the initial state in the OPCS and the covariance matrix for the initial state in the LSS.
Next, it is shown that we can design an approximate inverse system (named smoothed inverse system) having a meaning of the least-squares smoothing for systems with the same input-output dimensions. This design is done using a designing method for a sub-optimal preview control system (named SPCS) with finite preview actions in the infinite control interval and is useful for non-minimum phase systems.
We also show that the smoothed inverse system approaches the inverse system in the limit where R tends to zero, where R denotes a weighting matrix for the quadratic form of manipulated variables used in the LQ design technique.
