Event-triggered control for semi-global stabilisation of systems with actuator saturation

abstract

This paper investigates the problem of event-triggered control for semi-global stabilisation of null controllable systems subject to actuator saturation. First, for a continuous-time system, novel event-triggered low-gain control algorithms based on Riccati equations are proposed to achieve semi-global stabilisation. The algebraic Riccati equation with a low-gain parameter is utilised to design both the event-triggering condition and the linear controller; a minimum inter-event time based on the Riccati ordinary differential equation is set a priori to exclude the Zeno behaviour. In addition, the high–low gain techniques are utilised to extend the semi-global results to event-based global stabilisation. Furthermore, for a discrete-time system, novel low-gain and high–low-gain control algorithms are proposed to achieve event-triggered stabilisation. Numerical examples are provided to illustrate the theoretical results.

Keywords:

• Actuator saturation
• event-triggered control
• Riccati equation
• semi-global stabilisation

Acknowledgements

The authors would like to thank the Senior Editor and the anonymous reviewers for their insightful suggestions. This work was supported in part by the National Natural Science Foundation of China under Grant 61374053 and in part by the Hong Kong University Committee on Research and Conference Grants under Grant 201309176141.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant number 61374053]; Hong Kong University Committee on Research and Conference Grants [grant number 201309176141].