Event-triggered and self-triggered control for linear systems based on reachable sets

• Autores: Florian David Brunner, W.P.M.H. Heemels, Frank Allgöwer
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 101, 2019, págs. 15-26
• Idioma: inglés
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• Resumen

  • We propose novel aperiodic control schemes for additively perturbed discrete-time linear systems based on the evaluation of set-membership conditions related to disturbance reachable sets. The goal is to reduce the rate of communication between the sensor and the actuator, while guaranteeing that a certain set in the state space is asymptotically stabilized. In particular, we prescribe this set to be the minimal robust positively invariant set under a given feedback law updated at every time, multiplied by a factor that acts as a tuning parameter. This way, we achieve a trade-off between the communication rate and the worst-case asymptotic bound on the system state in the closed-loop system. We employ a novel stability concept that captures how much the system dynamics are explicitly dependent on past system states. This allows us to quantitatively compare the stability properties guaranteed by an all-time updated (static) feedback controller with those guaranteed by a (dynamic) aperiodic controller. We use the proposed framework to design both event-triggered and self-triggered controllers under the assumption of state feedback or output feedback.