Anti-Disturbance Control for Nonlinear Systems Based on Interval Observer

This paper proposes a disturbance interval estimation approach for nonlinear systems. Distinct from the conventional estimation schemes aiming to estimate the magnitude of the disturbance, the disturbance interval estimation approach is capable of approximating the time-varying upper and lower boundaries for the disturbance. To achieve this, the dynamics of the boundary estimation errors are constructed as positive systems by introducing a time-invariant coordinate transformation. The boundary estimation errors are guaranteed to be nonnegative and bounded. Then, the generated interval is capable of covering all possible values of the current disturbance and the interval width can provide a quantized guidance on the estimation accuracy at any time. Furthermore, a general antidisturbance control scheme is summarized in light of the proposed disturbance interval estimation approach. As an illustrative case, an antidisturbance control method is developed by integrating the proposed estimation approach and the sliding mode control. Finally, the proposed disturbance interval estimation approach and the anti-disturbance control method are demonstrated through both the numerical and the experimental validation.