Regulation of Non-Minimum-Phase Nonlinear Systems Using Slow Integrators

This paper focuses on the regulation problem for non-minimum-phase nonlinear systems with slow integrators, high-gain feedback and high-gain observer. The developed methodology involves four steps: At first, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in [11]. Then we use high-gain feedback to stabilize the original system, which is able to recover the performance of the auxiliary system by choosing the gain high enough. In the third step, with a condition on the dc steady-state input-output map, a slow integrator is added that enforces the objective of regulation. At last, we extend the methodology into the output feedback case by utilizing the extended high-gain observer to estimate the derivatives of the output as well as one unknown term including system uncertainties. The use of the observer recovers the performance under full-information feedback. The effectiveness of such methodology is demonstrated on the linearized inverted pendulum on a cart model (LIPC-model).