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Event-triggered and self-triggered control for linear systems based on reachable sets. (English) Zbl 1415.93170

Summary: 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.

MSC:

93C65 Discrete event control/observation systems
93C55 Discrete-time control/observation systems
93B03 Attainable sets, reachability
93C05 Linear systems in control theory
93B52 Feedback control
93D20 Asymptotic stability in control theory

Software:

CPLEX; YALMIP; MPT
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Full Text: DOI

References:

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