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

Abstract

This paper considers the stabilization of nonlinear continuous-time dynamical systems employing periodic eventtriggered control (PETC). Assuming knowledge of a stabilizing feedback law for the continuous-time system with a certain convergence rate, a dynamic, state dependent PETC mechanism is designed. The proposed mechanism guarantees on average the same worst case convergence behavior except for tunable deviations. Furthermore, a new approach to determine the sampling period for the proposed PETC mechanism is presented. This approach as well as the actual trigger rule exploit the theory of non-monotonic Lyapunov functions. An additional feature of the proposed PETC mechanism is the possibility to integrate knowledge about packet losses in the PETC design. The proposed PETC mechanism is illustrated with a nonlinear numerical example from literature. This paper is the accepted version of [1], containing also the proofs of the main results.

Model-Based Nonlinear Periodic Event-Triggered Control for Continuous-Time Systems with Sampled-Data Prediction

“…This allows the implementation of the x dynamics even on simple hardware. Zero-order hold (ZOH) feedback is a special case of the prediction with f p (x) = x and resembles the setup of [18].…”

“…We denote subsequently the maximum admissible sampling period such that (8) can be guaranteed as σ-MASP. The following proposition, that is taken from [18] can be used to guarantee satisfaction of (8) without explicit knowledge S(t, x 0 ). Proposition 1 (Proposition 3 from [18]): Consider two constants C 1 , C 2 ∈ R ≥0 , and S(t, x 0 ) defined by (7).…”

“…In this section, we first recap some results from [6] and [18]. Then, we extend a sufficient stability condition for DDS based on non-monotonic Lyapunov functions from [20] to the setup of this paper.…”

“…Preliminary Results from [6] and [18] First, we recap from [6] 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 [6] and [18] to design PETC mechanisms and to compute a lower bound on the σ-MASP for which stability and the convergence criterion ( 8) can be guaranteed. We will use the bound on the time derivative of V γ (x(t)) for the design of the MB-PETC mechanism.…”

“…We discuss how a suitable prediction model can be obtained. Finally, we demonstrate with a numerical example that the proposed approach can improve the system performance and nevertheless significantly reduce the required amount of communication in comparison to the prediction-free PETC mechanism from [18].…”