Lyapunov event-triggered control: a new event strategy based on the control

Abstract

Event-triggered control is a sampling strategy that updates the control value only when some events occur. An event is usually generated by an event-function that indicates if the control signal must be updated or not. If one excepts self-triggered implementation, event-triggered control requires the evaluation of the event function at each time instant. Unfortunately, in the literature of nonlinear system event-based control, computing the event function is more resource consuming than computing the control itself. Moreover, it requires the knowledge of a Lyapunov function that is not necessarily available. The purpose of this paper is to propose for affine nonlinear systems a new strategy for the choice of the event function that only requires the computation of the control. This reduces the complexity of computing the event and avoids to know the Lyapunov function.

Observer‐based event‐triggered control co‐design for linear systems

“…From (13) and the use of S-procedure, one obtains (15). Then, we conclude thatV (x(t)) < 0 and therefore…”

“…In this work, inspired by [15] and [21], the design of the event-triggering strategy for observer-based state feedback is proposed based on the decrease of a Lyapunov function. In the context of event-triggered control, the plant evolves in continuous time, whereas the control signal is updated depending on discretetime events, the resulting closed-loop system can be cast as hybrid or impulsive systems.…”

Lyapunov Event-Triggered Stabilization With a Known Convergence Rate

“…Also, we show that for each bounded region of the state space, self-triggered and periodic event-triggered controllers exist that provide stability for any initial condition from this region. Our approach substantially differs from the previous works [30], [40]- [42], [45]. Unlike [30], [45], we do not assume that CLF satisfies the ISS condition (8).…”

“…Whereas the condition (8) holds for linear systems [30] and some polynomial systems [45], in general it is restrictive and not easy to verify. Another approach to CLF-based design of event-triggered controllers has been proposed in [41], [42]. Discarding the ISS condition (8), this approach is based on Sontag's theory [4] and inherits its basic assumptions: first, the system has to be affine F (x, u) = f (x) + g(x)u, where f, g ∈ C 1 , second, Sontag's controller is admissible (u(x) ∈ U for any x).…”

Lyapunov Design for Event-Triggered Exponential Stabilization

“…A more recent result from [35] relaxes the ISS condition to a stronger version of usual asymptotic stability, however the control algorithm from [35], in general, does not ensure positive dwell time between the consecutive events, nor even the absence of Zeno behaviors. Another approach, based on Sontag's universal formula [36] and inheriting its basic limitations has been proposed in [28,29]. All of these results rely on restrictive assumptions, discussed in detail in Section 2, and do not allow to estimate the convergence rate efficiently.…”