Stabilizing Transmission Intervals for Nonlinear Delayed Networked Control Systems

Abstract

In this article, we consider a nonlinear process with delayed dynamics to be controlled over a communication network in the presence of disturbances and study robustness of the resulting closed-loop system with respect to network-induced phenomena such as sampled, distorted, delayed and lossy data as well as scheduling protocols. For given plant-controller dynamics and communication network properties (e.g., propagation delays and scheduling protocols), we quantify the control performance level (in terms of L p -gains) as the transmission interval varies. Maximally Allowable Transfer Interval (MATI) labels the greatest transmission interval for which a prescribed L p -gain is attained. The proposed methodology combines impulsive delayed system modeling with Lyapunov-Razumikhin techniques to allow for MATIs that are smaller than the communication delays. Other salient features of our methodology are the consideration of variable delays, corrupted data and employment of modelbased estimators to prolong MATIs. The present stability results are provided for the class of Uniformly Globally Exponentially Stable (UGES) scheduling protocols. The well-known Round Robin (RR) and Try-Once-Discard (TOD) protocols are examples of UGES protocols. Finally, two numerical examples are provided to demonstrate the benefits of the proposed approach. * D. Tolić is with Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia. S. Hirche is with the Chair

Robustness of Nonlinear Control Systems to Network-Induced Imperfections

“…A nonzero bias is caused by noisy and corrupted data [7,9]. Hence, when the data is not noisy or corrupted, we say "L p -stability" rather than "L p -stability with bias 0".…”

“…With the advent of more advanced hardware and software components, modern control systems are frequently being implemented over a shared (wired or wireless) resource-constrained communication network [1][2][3][4][5][6][7][8][9]. In particular, spatially distributed sensors, controllers and actuators in such control systems, termed Networked Control Systems (NCSs), do not exchange information through dedicated point-to-point connections.…”

“…Delays greater than the transmission intervals are called large delays. Taking the utilized robustness tool into account, other approaches pertaining to robustness of NCSs can be classified as: i) small-gain theorem approaches [7][8][9][11][12][13]; ii) dissipativity and passivity-based approaches [14]; and iii) Input-to-State Stability (ISS) approaches [15][16][17]. Since the corresponding robustness notions are distinct properties for nonlinear (delayed) dynamic systems, each work sheds different light on the NCS robustness problem for a specific class of NCSs.…”

“…Similar observations can be made with respect to other related works (see [6], [11], [14-19, 22, 23] and the references therein). In comparison with [9], the present work focuses entirely on NCS robustness even though similar mathematical tools are utilized. The conference version of this article is [24].…”

Impulsive stabilization for linear neutral‐type time‐delay systems

“…that the impulsive system approach has found useful applications in the analysis and modeling of hybrid control systems, including sampled-data control systems, [10][11][12] networked control systems, 13,14 reset control systems, 15,16 and event-triggered control systems. 17 The most popular method for stability analysis of impulsive systems is still the Lyapunov approach.…”