Event-based sampling algorithm for setpoint tracking using a state-feedback controller

Abstract

Event-based control techniques are investigated for output reference tracking in the case of linear time-invariant systems. In event-based control, the controller remains at rest if the system is behaving according to some predefined conditions, the feedback loop being closed only when the system states violate these conditions. In this work a reference system, which consists in the continuously-controlled version of the system under study, is employed. Based on the difference between the state of the event-triggered system and that of the reference system, we define a Lyapunov-like function, and show that if we can keep this function confined to a certain region, the tracking error would also be bounded. The trespassing of this function outside of the desired region is used as an event-triggering condition.

Event-triggered stabilizing controllers based on an exponentially decreasing threshold

“…In classical control, stability necessitates V to be decreasing in time. However, as proved in [12], if we allow V (x) to be locally increasing, the stability property can be maintained with an event-triggered control law. Moreover, this allows to obtain events that are sparser in time.…”

“…We have seen in [12] that a constant event-triggering condition achieves only practical stability. We know from [13] that asymptotic stability is achieved through a decaying-intime triggering condition.…”

“…Proof. The proof follows the same scheme as in [12] but here the problem is simpler as we do not attempt to track a reference signal that may contain discontinuities.…”

Event-Based Integral Control for Output Disturbance Rejection

“…The sequel is very similar to the arguments used in [11]. Two symmetric positive definite matrices P and Q are defined via the Lyapunov equation A T a P + P A a = −Q.…”

“…Unlike to [10], the objective is to drive the system to follow a predefined trajectory in the presence of an unknown low-frequency output disturbance. As in [11], the state of the system is compared to the state of a continuously-controlled reference system. But here, the disturbance renders this comparison difficult since it is a priori unknown to the reference system.…”