Trajectory tracking model-following control using Lyapunov redesign with output time-derivatives to compensate unmatched uncertainties

We study trajectory tracking for flat nonlinear systems with unmatched uncertainties using the model-following control (MFC) architecture. We apply state feedback linearisation control for the process and propose a simplified implementation of the model control loop which results in a simple model in Brunovsky-form that represents the nominal feedback linearised dynamics of the nonlinear process. To compensate possibly unmatched model uncertainties, we employ Lyapunov redesign with numeric derivatives of the output. It turns out that for a special initialisation of the model, the MFC reduces to a single-loop control design. We illustrate our results by a numerical example.

💡 Research Summary

The paper addresses the problem of trajectory tracking for flat nonlinear systems that are subject to unmatched uncertainties—disturbances that do not appear directly in the input channel. Starting from the system model
(\dot x = f(x) + g(x)u + \Delta(x),; y = h(x))
with relative degree (r=n), the authors first apply state‑feedback linearisation to obtain Brunovsky‑form coordinates (\xi =