H ∞ control of networked control systems with packet disordering with an improved prediction-based method

Abstract

This paper is concerned with H ∞ control of networked control systems (NCSs) with both network-induced delay and packet disordering taken into account. A switching-based method depends on different cases of prediction numbers is presented to model the NCSs as a switched system. With the application of an improved prediciton-based method to compensate for the time delay and packet disordering, H ∞ controller is designed by solving the linear matrix inequalities (LMIs). The proposed method can be applied variously due to all kinds of prediciton numbers of the consective disordering packet have been considered, which means that our techniques are less conservative than existing literatures. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching-based method and the improved prediction-based H ∞ controller design synthesis.

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

“…Define p = max{ p (⋅)}, and replace p ( k ) and p ( k + 1) with p , we can obtain the packet‐disordering‐independent results as presented in . In other words, the methods in and are special cases of ours. Remark Given feedback gains are consistent, i.e. , the controller design is delay‐ and packet‐disordering‐independent similar to the techniques in existing literature (see details in and ).…”

“…The effectiveness of the prediction‐based method will be verified in the final examples. Remark A similar prediction‐based method is applied earlier in and . However, it is worth commenting that the problem of networked output tracking control considered in this paper is not covered in and or any other existing reference. Remark For consecutive instants, the prediction numbers are allowed to be different in Algorithm , however the method presented in chooses the maximum prediction number of consecutive packet disordering as the same prediction number for the two consecutive instants. For example, given the prediction numbers of consecutive packet disordering are p ( k ) and p ( k + 1), respectively, then the prediction number is defined as p = max{ p ( k ), p ( k + 1)} in , which is illustrated more conservative in later numerical examples.…”

“…Thus, according to Algorithm , the evolution of system can be described as the following switched system: where ( i , j ) ∈ Θ = [1, 3] × [1, 3],, are obtained from replacing by Δ sj = Γ 1 K sj , s = 1, 2 in E i ( j k ) and F i ( j k ), respectively. Remark Based on different cases of the consecutive prediction numbers as described in , we presented three kinds of augment NCSs, and formed a switched system. In addition, to improving the method in , we present Algorithm for the packet‐disordering‐dependent controller design.…”

“…Remark Based on different cases of the consecutive prediction numbers as described in , we presented three kinds of augment NCSs, and formed a switched system. In addition, to improving the method in , we present Algorithm for the packet‐disordering‐dependent controller design. Because the prediction number is dependent on time delay and packet disordering, the switched system formulated above is delay‐ and packet‐disordering‐dependent, and the controller is based on the packet disordering in the last transmission interval.…”

“…Remark 3. A similar prediction-based method is applied earlier in [20] and [27]. However, it is worth commenting that the problem of networked output tracking control considered in this paper is not covered in [20] and [27] or any other existing reference.…”