Interval-based sliding mode control and state estimation for uncertain systems

Sliding mode control is one possible technique for the guaranteed stabilization of nonlinear systems by means of feedback control. This design approach makes use of a suitable Lyapunov function with which also parameter uncertainties and bounded measurement errors can be handled reliably during the parameterization of the control law. However, a classical design of sliding mode control laws requires conservative estimates for the influence of uncertain variables which commonly leads to large amplitudes of the switching part in the sliding mode control law. Unfortunately, this corresponds to undesirable noise and actuator wear. In this paper, an interval arithmetic extension of sliding mode control is presented which allows for a reduction of both chattering phenomena and control amplitudes but still stabilizes the system dynamics in a provable way. The paper is concluded by an illustrative example for which stability properties of typical regularization strategies for sliding mode control laws are analyzed with the help of interval arithmetic. Moreover, a representative interval arithmetic implementation of a sliding mode state and disturbance observer is presented.