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

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...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2024-12, Vol.69 (12), p.8782-8789
Main Authors: Wang, Yujie, Xu, Xiangru
Format: Article
Language:English
Subjects:
Closed loop systems
Control barrier functions (CBFs)
Control systems
disturbance observer (DOB)
Disturbance observers
Estimation error
immersion and invariance
Invariance
Nonlinear control
Partial differential equations
safe control
Safety
Submerging
System effectiveness
Systematics
Vectors
Citations: Items that this one cites
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2024.3416323