Adaptive sliding controller synthesis for non-linear systems

Classical 'sliding mode control', as investigated mostly in Soviet literature, features excellent robustness properties in relation to parametric uncertainty, but presents several important drawbacks that severely limit its practical applicability. These drawbacks, including large control authority and control chattering, were remedied by Slotine and Sastry (1983) and Slotine (1984) by replacing control switching at a fixed sliding surface by a smooth control interpolation in a boundary layer neighbouring a time-varying sliding surface. This avoids the excitation of high-frequency unmodelled dynamics, and leads to an explicit trade-off between model uncertainty and controller tracking performance. The present paper examines how to further improve performance by effectively coupling on-line parameter estimation to sliding controller design. The boundary layer concept leads to a compact measure of the quality of parameter estimation, and provides a consistent rule on when to stop adaptation. The approach is demonstrated by simulations.