Uncertainty observer-based robust tracking control for high-order nonlinear systems using forwarding technique

ABSTRACT

Based on uncertainty observers, we develop a robust tracking control approach for high-order nonlinear systems subject to uncertainties satisfying mismatched condition. In this study, by combining with forwarding technique, uncertainty observers are designed to estimate uncertainties including parameter perturbations and external disturbances in a bottom-up way; at the same time, the convergence rate of estimate error of uncertainty observers is analysed in detail. The insensitivity to uncertainties for each manifold, no need of a prior knowledge on the bound of the uncertainty and the feasibility of practical implementation are three advantages of the proposed scheme. Moreover, approximate error of uncertainty observer can be made sufficiently small by tuning the parameters. The design procedures are elaborated and the boundedness of all trajectories of the closed-loop systems is guaranteed. Two examples are illustrated, highlighting the superiority of the proposed methodology via comparison with other control strategies.

KEYWORDS:

• High-order nonlinear systems
• robust tracking control
• forwarding technique
• uncertainty observer
• complexity of explosion

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Remark that the superscript [·] denotes the order of the target system.

2. Throughout the paper, the induced matrix 2-norm is meant: $X\in {\mathbb{R}}^{n\times n}\to \parallel X\parallel =\sqrt{{\lambda }_{\max }\left(X^{\mathrm{T}}X\right)}$, where λ_max(·) denotes the maximum eigenvalue of a square matrix.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant Numbers 51275107, 61304006 and 61273095]; the Innovative Team Program of the National Natural Science Foundation of China [Grant Number 61021002].