Lyapunov Event-Triggered Stabilization With a Known Convergence Rate

Abstract

A constructive tool of nonlinear control systems design, the method of Control Lyapunov Functions (CLF) has found numerous applications in stabilization problems for continuoustime, discrete-time and hybrid systems. In this paper, we address the fundamental question: given a CLF, corresponding to the continuous-time controller with some predefined (e.g. exponential) convergence rate, can the same convergence rate be provided by an event-triggered controller? Under certain assumptions, we give an affirmative answer to this question and show that the corresponding event-based controllers provide positive dwelltimes between the consecutive events. Furthermore, we prove the existence of self-triggered and periodic event-triggered controllers, providing stabilization with a known convergence rate.

Nonlinear Dynamic Periodic Event-Triggered Control with Robustness to Packet Loss Based on Non-Monotonic Lyapunov Functions

“…In the second subsection, we state a sufficient condition for the convergence criterion (9) that is easier to verify than the criterion itself. In the last subsection, we recap a technical result and a set of assumptions from [15], which will be useful for designing the PETC mechanism and for constructing a lower bound on the σ-MASP.…”

“…In this subsection, we recap from [15] how a time dependent and state independent upper bound on the time derivative of V γ (x(t)) can be computed. This bound is used in [15] to compute a lower bound on the σ-MASP for which the decrease of V γ (x(t)) with a chosen convergence rate according to (7) can be guaranteed.…”

“…Assumption 4 resp. Lemma 1 from [15]) For the chosen c ∈ R >0 , there is a positive definite function…”

“…For specific classes of nonlinear systems, PETC is investigated in [13], [14]. In [15] it is shown, that ETC and PETC with a known (and chosen) convergence rate for nonlinear systems can be designed, provided that a control Lyapunov function is known for the continuous-time system.…”

A Sliding Mode Observer Approach for Attack Detection and Estimation in Autonomous Vehicle Platoons using Event Triggered Communication

“…Vehicles in a CACC platoon measure relative position and velocity of the preceding vehicle, and also communicate (see figure 1) in order to attain string stability, which is an important property resulting in dampening of velocity changes down the platoon [6]. The reliance of CACC platoons on inter-vehicle wireless communications, be it periodic or event-triggered [7]- [9], may expose them to the same kind of threats as other networked control systems or Cyber-Physical Systems (CPS), such as Denial of Service (DoS), routing, replay and stealthy data injection attacks (see [10], [11]). Indeed, vulnerabilities of Vehicle-to-Vehicle (V2V) networks to cyber attacks have been investigated in [12]- [15].…”