Sliding control of non-linear systems containing time-varying uncertainties with unknown bounds

The sliding controller is very effective in dealing with system uncertainti es defined in compact sets. If the bounds of the uncertainties are not avai lable, the adaptive sliding controller might be designed. One restriction f or the adaptive sliding scheme is that the unknown parameter should be cons tant, which is not always satisfied in practice. For a non-linear system wi th general uncertainties (i.e. time varying with unknown bounds), both the traditional sliding control and adaptive sliding control do not work proper ly. This paper proposes a new sliding control scheme for non-linear systems containing time-varying uncertainties with unknown bounds. The uncertainti es are assumed to be piecewise continuous functions of time and satisfy the Dirichlet conditions. By representing these uncertainties in finite-term F ourier series, they can be estimated by updating the Fourier coefficients. Since the coefficients are time-invariant, update laws are easily obtained from the Lyapunov approach to guarantee output error convergence. Computer simulations are performed to show efficacy of the proposed schemes.