Prescribed Performance Tracking Control of Nonlinear Systems with Unknown Control Directions

This work addresses the fuzzy adaptive tracking control problem for a larger class of uncertain r-Norm nonlinear systems whose control directions are partial unknown. Different from the existing literatures, both no a priori knowledge on the control direction is needed, and some specified performances (e.g. maximum overshoot and convergence rate) are taken into account simultaneously in this paper. To pursue this, the adding one power integrator method is skillfully incorporated into the design control scheme and the new design involves an extension of conditional inequality appearing in the state of the art which enables multiple Nussbaum gain functions to achieve control robustness while ensuring the closed-loop stability. It is proved that all the signals in the resulting closed-loop system are bounded and that the tracking errors converge to a small residual set with the prescribed performance bounds. The effectiveness of the proposed approach is validated by simulation result.