Inverse optimal design of input-to-state stabilisation for affine nonlinear systems with input delays

ABSTRACT

We establish robustness of the predictor feedback control law to perturbations appearing at the system input for affine nonlinear systems with time-varying input delay and additive disturbances. Furthermore, it is shown that it is inverse optimal with respect to a differential game problem. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation and an appropriate Lyapunov functional. A single-link manipulator subject to input delays and disturbances is given to illustrate the validity of the proposed method.

KEYWORDS:

• Delay affine systems
• predictor feedback
• input-to-state stabilisation
• disturbance attenuation
• inverse optimality
• robustness

Acknowledgments

The authors thank the anonymous reviewers for their many helpful suggestions. The authors are grateful for the support of the National Natural Science Foundation of China (Grant numbers 61773350, 61374077, 61473265, 61503107,U1404610, and the Natural Science Foundation of Zhejiang Province of China [grant number LY17F030001).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 61773350], [grant number 61374077], [grant number 61503107], [grant number 61473265], [grant number U1404610] and the Natural Science Foundation of Zhejiang Province of China [grant number LY17F030001].