Robust adaptive control of strict-feedback nonlinear systems with unmodelled dynamics and time-varying delays

ABSTRACT

This paper presents a novel robust adaptive neural control scheme which can be taken as a robustification of the adaptive backstepping design. The considered class of uncertainties contains unknown non-symmetric dead-zone inputs, time-varying delay uncertainties, unknown dynamic disturbances and unmodelled dynamics. The radial basis function neural networks (RBFNNs) are employed to approximate the unknown nonlinear functions obtained by Young’s inequality. By constructing exponential Lyapunov-Krasovskii functionals, the upper bound functions of the time-varying delay uncertainties are compensated for. Using Young’s inequality and RBFNNs, the assumptions with respect to unmodelled dynamics are relaxed. It is demonstrated that the proposed controller guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error eventually converges to a neighbourhood of zero.

Keywords:

• Time-varying delays
• radial basis function neural network
• adaptive control
• Young’s inequality
• exponential Lyapunov-Krasovskii functionals

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61174076, 61374086, 61374087, 61573007, the Program for Changjiang Scholars and Innovative Research Team in University under Grant IRT13072, and a project funded by the priority academic program development of Jiangsu Higher Education Institutions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant numbers 61174076, 61374086, 61374087, 61573007]; Program for Changjiang Scholars and Innovative Research Team in University [grant number IRT13072]; Jiangsu Higher Education Institutions.