Output regulation problem and solution for LTV minimum phase systems with time-varying exosystem

Output regulation problem is to design a dynamic feedback controller that rejects/follows the unknown disturbance/reference asymptotically assuming that the disturbance/reference is generated by a known model (called exosystem). Although the model is known, the disturbance/reference is still unknown because the initial condition of the exosystem is unknown. It has been studied very actively since the seminal work by Francis in 1977 [8], and up to now, we have quite complete solution in the conventional sense. However, most results assume that the exosystem is time-invariant. Although nonlinear exosystem has also been considered, the time-varying exosystem has not been incorporated because of the Poisson stability required to the nonlinear exosystem. In this paper, we extend output regulation theory into the case of time-varying linear systems with time-varying linear exosystems. This is enabled by considering 'differential regulator equation' rather than the classical (algebraic) regulator equation. While the differential regulator equation was also employed by Zhang and Serrani in 2005 [7], who solved the output regulation problem with the periodic exosystem, we use it for deriving an explicit solution of the class of minimum-phase systems having general time-varying exosystem. As an application, we solve the track following problem for an optical disc drive system whose spindle motor is accelerating or decelerating. This case leads to the disturbance having time-varying frequency, which turns into the time-varying exosystem. It seems that this result can be applied to robotics/mechatronic systems control.