Robust Adaptive Control of Polynomial Lower-Triangular Systems with Dynamic Uncertainties

This paper investigates the problem of robust adaptive control for a class of nonlinear systems, called polynomial lower-triangular form (pLTF), which not only expands LTF to a more general case, but also consists of three types of uncertainties: parametric uncertainties, uncertain nonlinearities and dynamic uncertainties. The proposed design approach joins the tool of power integrator with small-gain techniques. Firstly, via the recursive design, an adaptive controller is formulated to render the systems robust with respect to static uncertainties. Secondly, by the small-gain theorem, we show under the condition the adaptive controller guarantees the robustness property of the systems in the presence of dynamic uncertainties. Finally, an example is provided to illustrate the validity of the design