Adaptive Control of Flat MIMO Nonlinear Systems With Additive Disturbance

In this paper, two controllers are developed for flat multi-input/multi-output nonlinear systems. First, a robust adaptive controller is proposed and proven to yield semi-global asymptotic tracking in the presence of additive disturbances and parametric uncertainty. In addition to guaranteeing an asymptotic output tracking result, it is also proven that the parameter estimate vector is driven to a constant vector. In the second part of the paper, a learning controller is designed and proven to yield a semi-global asymptotic tracking result in the presence of additive disturbances where the desired trajectory is periodic. A continuous nonlinear integral feedback component is utilized in the design of both controllers and Lyapunov-based techniques are used to guarantee that the tracking error is asymptotically driven to zero. Numerical simulation results are presented for both controllers.