Forwarding-based trajectory tracking control for nonlinear systems with bounded unknown disturbances

There are only a few methods for controlling high-order nonlinear systems, except for standard backstepping technique. Due to the fact that I&I theory proposed by Astolfi and Ortega is able to accomplish the system immersion by selecting a lower-order target system and a vital mapping, a bottom-up recursive procedure for designing tracking control laws for a class of n-dimensional strict-feedback nonlinear systems is focused in our work. The required mappings are transformed into virtual control inputs, and system order reduction is realized as design step is implemented repetitively. A first-order filter is employed at each step to compute analytic derivatives of mappings. The benefit of our proposed algorithm can not only improve the computation efficiency to simplify all controls’ forms, but also suppress the high-frequency noise. While the off-the-manifold coordinate is rendered insensitive to the time-varying and bounded but unknown disturbance, the robust stability can be ultimately guaranteed. A quadrotor helicopter is used to show designing procedures and controller performance via various simulations.