Constrained control for systems on matrix Lie groups with uncertainties

In this paper, the constrained control of systems evolving on matrix Lie groups with uncertainties is considered. The proposed methodology is composed of a nominal Model Predictive Control (MPC), and a feedback controller. The previous work on the control of systems on manifolds is applied to design...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2023-03, Vol.33 (5), p.3285-3311
Main Authors: Shi, Chuanbeibei, Yu, Yushu, Ma, Yuwei, Chang, Dong Eui
Format: Article
Language:English
Subjects:
Attitude control
Constraints
Control methods
Control systems
Euclidean geometry
Euclidean space
Feedback control
Lie groups
Mathematical analysis
Mathematical models
matrix Lie group
Methodology
Predictive control
Rigid structures
robust control
Tracking errors
tube‐based model predictive control
Uncertainty
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Summary:In this paper, the constrained control of systems evolving on matrix Lie groups with uncertainties is considered. The proposed methodology is composed of a nominal Model Predictive Control (MPC), and a feedback controller. The previous work on the control of systems on manifolds is applied to design the nominal MPC, which generates the nominal trajectory. In the nominal MPC, the state and input constraints on the Lie group are transformed into the constraints on the Euclidean space. While to deal with uncertainties, the feedback control used to track the nominal trajectory is designed directly on the Lie group. The tracking error in the feedback control is proved to be bounded in invariant sets, which are further used to revise the constraints in nominal MPC. We prove that the input‐to‐state stability of the entire system under the proposed control methodology with respect to the disturbances can be achieved. The proposed methodology is applied to the constrained attitude control of rigid bodies with uncertainties. In the application example, the detailed mathematical proof and the comparative numerical simulation are presented to demonstrate the feasibility of the proposed methodology.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.6574