Adaptive Output Regulation for Discrete-time Linear Systems with an Uncertain Exosystem

This paper studies the output regulation problem for discrete-time linear systems subject to an uncertain exosystem. The design involves two online estimation algorithms. The first one is to estimate the unknown parameters of the exosystem, and the second one is to estimate the solution to the regulator equations based on the estimated system matrix of the exosystem. Combining these two algorithms gives rise to an iterative solution that converges exponentially to some exact solution to the regulator equations. Finally, by integrating these two algorithms with the feedforward control approach, both dynamic state feedback and dynamic output feedback control laws are synthesized to solve the problem.