Observation and output adaptive tracking for a class of nonlinear non-minimum phase systems

In this paper, the output tracking problem for a class of systems with unstable zero dynamics is addressed. The state is assumed not measurable. The output of the dynamical system to be controlled has to track a signal, which is the sum of a known number of sinusoids with unknown frequencies, amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviours of the internal dynamics. The proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state; therefore, a nonlinear observer is needed. Due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states, adaptive indirect methods are applied.