Adaptive stabilisation of ODE systems via distributed effect of uncertain diffusion-dominated actuator dynamics

ABSTRACT

Adaptive stabilisation is investigated for ordinary differential equation systems via distributed effect of uncertain diffusion-dominated actuator dynamics. The presence of the unknowns/uncertainties and the distributed effect makes the system under investigation more general and representative than those of the related literature, and moreover yields the ineffectiveness of the existing methods on this topic. By constructing an invertible spatial and time-varying state transformation, the original closed-loop system is first changed into a target system, from which the design of parameter updating law and the analysis of the closed-loop system performance become more convenient. Then, by Lyapunov method and adaptive compensation technique, an adaptive stabilising controller is successfully constructed, which guarantees that the original system states converge to zero while other closed-loop system states are bounded. A simulation example is provided to validate the proposed method.

KEYWORDS:

• Adaptive stabilisation
• actuator dynamics
• distributed effect
• diffusion equation

Acknowledgments

The authors thank the editor, the associate editor for the time and efforts spent in handling the article. The authors are also indebted to the anonymous referees for their valuable comments which have greatly improved the quality and presentation of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundations of China [grant number 61403327], [grant number 61325016], [grant number 61273084], [grant number 61233014].