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arXiv · 2309.06718

Immersion and Invariance-based Disturbance Observer and Its Application to Safe Control

Yujie Wang·Xiangru Xu
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Abstract

When the disturbance input matrix is nonlinear, existing disturbance observer design methods rely on the solvability of a partial differential equation or the existence of an output function with a uniformly well-defined disturbance relative degree, which can pose significant limitations. This note introduces a systematic approach for designing an Immersion and Invariance-based Disturbance Observer (IIDOB) that circumvents these strong assumptions. The proposed IIDOB ensures the disturbance estimation error is globally uniformly ultimately bounded by approximately solving a partial differential equation while compensating for the approximation error. Furthermore, by integrating IIDOB into the framework of control barrier functions, a filter-based safe control design method for control-affine systems with disturbances is established where the filter is used to generate an alternative disturbance estimation signal with a known derivative. Sufficient conditions are established to guarantee the safety of the disturbed systems. Simulation results demonstrate the effectiveness of the proposed method.

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Yujie Wang, Xiangru Xu. 2023-09-13. Immersion and Invariance-based Disturbance Observer and Its Application to Safe Control. https://arxiv.org/abs/2309.06718

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