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Asymptotic tracking of a nonminimum phase nonlinear system with nonhyperbolic zero dynamics

A two-cart with inverted-pendulum system is a nonlinear nonminimum-phase system with nonhyperbolic zero dynamics. This system was introduced to study the output regulation problem for nonlinear systems with nonhyperbolic zero dynamics. In this paper, we will first note that nonhyperbolicity is not necessary to the applicability of the output regulation theory. In particular, for the two-cart with inverted-pendulum system, the problem of output regulation for a class of sinusoidal reference input is actually solvable notwithstanding the presence of the nonhyperbolicity. A control law based on the standard output regulation theory is then synthesized and its performance is illustrated through computer simulation.