Asymptotic adaptive regulation of parametric strict-feedback systems with additive disturbance

This paper deals with the regulation of uncertain, multi-input/multi-output, nonlinear parametric strict-feedback systems of nth order subjected to additive disturbances. A continuous adaptive control law is proposed using a modified backstepping design that ensures the output is asymptotically driven to zero. Despite the disturbance, the adaptation law does not need a standard leakage term to ensure the aforementioned stability result; rather, we use a dynamic robust control mechanism and a recently-developed projection operator that is arbitrarily many times continuously differentiable. A numerical example illustrates the main result.