Continuous fractional sliding mode-like control for exact rejection of non-differentiable Hölder disturbances

Exploiting algebraic and topological properties of differintegral operators as well as a proposed principle of dynamic memory resetting, a uniform continuous sliding mode controller for a general class of integer order affine non-linear systems is proposed. The controller rejects a wide class of disturbances, enforcing in finite-time a sliding regime without chattering. Such disturbance is of Hölder type that is not necessarily differentiable in the usual (integer order) sense. The control signal is uniformly continuous in contrast to the classical (integer order) discontinuous scheme that has been proposed for both fractional and integer order systems. The proposed principle of dynamic memory resetting allows demonstrating robustness as well as: (i) finite-time convergence of the sliding manifold, (ii) asymptotic convergence of tracking errors, and (iii) exact disturbance observation. The validity of the proposed scheme is discussed in a representative numerical study.