Multiple filtered high-gain observers-based robust control for mixed-order fully actuated systems

This paper presents a robust controller design framework based on multiple filtered high-gain observers (MFHGO) for mixed-order fully actuated systems (MOFASs) subject to incomplete state measurements, model uncertainties, and measurement noise. The proposed MFHGO employs multiple filtered high-gain observers (FHGOs) operating in parallel, where their state estimation outputs are adaptively weighted and fused through a recursive least squares (RLS) algorithm to obtain the final state estimates. Each FHGO incorporates an embedded filter structure with the order of the high-gain parameter not exceeding 2, while enabling arbitrary eigenstructure configuration of the estimation error system through systematic design parameter selection. This structural design effectively mitigates the peaking phenomena, numerical implementation issues, and measurement noise sensitivity commonly encountered in traditional high-gain observers (HGOs). Furthermore, for the MFHGO-based robust controller design for mixed-order fully actuated systems, the design parameters can be systematically determined using parameterized design methods. Compared with existing methods that are limited to single-order fully actuated systems, the proposed controller offers broader applicability. Finally, the effectiveness of the proposed MFHGO-based fully actuated robust controller is validated through simulation studies on a two-link robotic manipulator.