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

TL;DR

This paper presents a novel Immersion and Invariance-based Disturbance Observer (IIDOB) that overcomes limitations of existing methods for nonlinear disturbance input matrices, and integrates it with control barrier functions for safe control of disturbed systems.

Contribution

It introduces a systematic IIDOB design that avoids strong assumptions and integrates it with safe control frameworks for improved disturbance handling.

Findings

IIDOB ensures globally bounded disturbance estimation error.

The integrated safe control method guarantees system safety under disturbances.

Simulation results validate the effectiveness of the proposed approach.

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.