Predictor-based networked control under uncertain transmission delays

Abstract

We consider state-feedback predictor-based control of networked control systems with large time-varying communication delays. We show that even a small controller-to-actuators delay uncertainty may lead to a non-small residual error in a networked control system and reveal how to analyze such systems. Then we design an event-triggered predictor-based controller with sampled measurements and demonstrate that, depending on the delay uncertainty, one should choose various predictor models to reduce the error due to triggering. For the systems with a network only from a controller to actuators, we take advantage of the continuously available measurements by using a continuous-time predictor and employing a recently proposed switching approach to event-triggered control. By an example of an inverted pendulum on a cart we demonstrate that the proposed approach is extremely efficient when the uncertain time-varying network-induced delays are too large for the system to be stabilizable without a predictor. IntroductionIn networked control systems (NCSs), which are comprised of sensors, controllers, and actuators connected through a communication medium, transmitted signals are sampled in time and are subject to time-delays. Most existing papers on NCSs study robust stability with respect to small communication delays (see, e.g., [2][3][4][5]). To compensate large transport delays, predictorbased approach can be employed. So far this was done only for sampled-data control with known constant delays [6,7]. In this paper we develop predictor-based sampled-data control for unknown time-varying delays.There are several works that study robustness (w.r.t. delay uncertainty) of a predictor-based continuous-time controller [8][9][10][11]. In these works the residual error that appears due to delay uncertainty can be made arbitrary small by reducing the upper bound of the uncertainty. However, this is not true for sampled-data systems, where an arbitrary small delay uncertainty may A. Selivanov (antonselivanov@gmail.com) and E. Fridman (emilia@eng.tau.ac.il) are with School of Electrical Engineering, Tel Aviv University, Israel.

State feedback control and delay estimation for LTI system with unknown input-delay

“…2 A similar result is also given in (Selivanov & Fridman, 2016, Appendix A, (A.5)-(A.6)) with the use of the Gronwall-Bellman Lemma.…”

An LMI condition for the robustness of constant-delay linear predictor feedback with respect to uncertain time-varying input delays

“…Many extensions have been reported (see, e.g., [14] and the references therein). These include the case of time-varying delay linear predictor feedback [16]; robustness with respect to disturbance signals [5]; truncated predictor [23]; predictor observers in the case of sensor delays [14]; predictors for nonlinear systems [3,15]; dependence of the delay on the state [2]; networked control [22]; and the boundary control of partial differential ⋆ This publication has emanated from research supported in part by a research grant from Science Foundation Ireland (SFI) under grant number 16/RC/3872 and is co-funded under the European Regional Development Fund and by I-Form industry partners. Corresponding author H. Lhachemi.…”

Delayed point control of a reaction–diffusion PDE under discrete-time point measurements

“…The main theoretical challenges caused by networked architecture are data sampling and transmission delays, which have been extensively studied for finite-dimensional plants. In particular, predictors, originally proposed for continuous-time measurements [3][4][5], have been extended to discrete-time measurements for both static [6][7][8][9] and dynamic feedback [10][11][12].…”