An <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e171" altimg="si10.svg"><mml:msub><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-consistent event-triggered control policy for linear systems
Mohammadhadi Balaghiinaloo, Duarte Antunes, W.P.M.H. Heemels
Abstract
In this article, we consider the design of an event-triggered ℓ2-control policy, for a setting where a scheduler is arbitrating state transmissions from the sensors to the controller of a discrete-time linear system. We start by introducing a periodic time-triggered ℓ2-controller for different transmission time-periods with a given ℓ2-gain bound using the minimax game-theoretical approach. After that, we propose an ℓ2-consistent event-triggered controller in the sense that it guarantees at least the same ℓ2-gain bound as the designed periodic time-triggered ℓ2-controller, however with a larger, or at most equal, average inter-transmission time. In practice, for typical disturbances, the proposed event-triggered scheme can lead to significant gains, both in terms of communication savings and disturbance attenuation, compared to periodic time-triggered policies, which is illustrated through a numerical example.