Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties (Q1765178)

An \(n\)-dimensional single-input single-output nonlinear control system with mismatched uncertainties is considered. An adaptive multiple-surface sliding controller is designed so that the output of the corresponding closed-loop system asymptotically converges to a smooth reference output (if the approximation errors can be ignored) while the other signals remain bounded. The key idea is to approximate all the uncertain terms by finite linear combinations of functions generating an orthonormal basis. The coefficients of these linear combinations are updated according to the conventional Lyapunov design. A simulation example is also presented.