On hold or drop out-of-order packets in networked control systems

Abstract

Holding or dropping out-of-order packets in the communications are two typical signal choosing schemes in networked control systems. However, neither of the two schemes can be claimed always superior to the other. To improve the control performance, a smart signal choosing scheme is proposed to determine whether to use the out-of-order packets. It is theoretically proved that improved performance can be obtained based on the proposed smart signal choosing scheme. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Introduction

Networked control systems (NCSs) involve communication patterns in which both information and control loops are closed through a real-time network. It has shown that NCSs are becoming increasingly important in industrial process due to their cost-effectiveness, reduced weight and power requirements, simple installation and maintenance [7], [25]. For details, see, for examples [4], [9], [16], [17], [20], [22], [24] and references therein.

Due to the introduction of the communication networks, the network-induced delays, data dropouts and out-of-order packets in the communication are inevitable [6]. Recently, there are extensive reports on NCSs with the network-induced delays and the data dropouts [2], [13], [14], [15], [21], [27], [29], [30]. For example, Peng et al. proposed a communication delay distribution dependent stabilization criterion for a networked T–S fuzzy system [13]. Quevedo et al. studied the input-to-state stability over unreliable networks [14]. Schenato compared the control performance while using zero or holding control input with lossy links in the NCSs [15]. However, there are few results concerning the effect of out-of-order packets in an NCS.

Notice that there are two general schemes to deal with the out-of-order packets (OOP) in the NCSs. In the first one, the input to a plant is set to be the latest arrived packet and is kept constant by a zero-order-holder (ZOH) until the next arrived packet [8], [11], [18]. Therefore, the latest arrived packet is used by the actuator no matter whether it is an out-of-order packet. We refer to this case as ZOH scheme; while in the second one, the ZOH at the actuator has the function to detect whether or not it is an out-of-order packet, and only the latest time-stamped packet is chosen as the input of the actuator [12], [13], [23], [31]. In line with the existing results, we refer to this case as Logic ZOH scheme. However, to the best of authors’ knowledge, there are no results in the literature concerning the differences between the above mentioned schemes in an NCS. Intuitively, dropping the out-of-order packets are more reasonable to improve the system performance, since the latest packet is closer to the latest calculated control input. However, fully dropping the out-of-order packets are unreasonable in an NCS, since: (i) for a stable closed-loop system, after the transient, it is no matter whether an OOP is chosen or not, since the system converges to its equilibrium eventually; and (ii) during the transient, an out-of-order packet leads to a delayed control input. As reported in [1], [10], the delayed control inputs have positive effects in some situations. In other words, there are some situations where the delay free feedback system is unstable while becoming stable due to the presence of appropriate delay. Compared with holding the out-of-order packets at the actuator, it remains unclear whether improved performance can be expected by fully dropping the out-of-order packets. These issues motivate the current study.

In this paper, we will model a discrete linear system controlled over a communication network as an input delay system and propose a stabilization criterion for the system under consideration. Then, for showing that neither ZOH scheme nor logic ZOH scheme is superior to the other, we will introduce two examples to compare the quadratic cost like performance index on the above mentioned schemes. Next, we will propose a smart ZOH signal choosing scheme to obtain the improved control performance. In particular, a theorem will also be provided to show the effectiveness of the proposed signal choosing scheme.

The main contribution of this paper is:

• To a given performance index, it is found that fully dropping or holding the out-of-order packets at the actuator is not helpful to improve the performance in an NCS.

• A smart signal choosing scheme is proposed to determine whether to use an out-of-order packet at the actuator. A theorem is provided to show that improved performance can be expected based on the above proposed scheme.

• Compared with some existing results [3], [28], the proposed stabilization criterion has the advantage of obtaining a larger allowable delay bound while depending on fewer number of linear matrix inequality (LMI) scalar decision variables.

The paper is organized as follows. System modeling and addressed problem are described in Section 2. The system analysis and synthesis criteria are given in Section 3. Section 4 gives two experimental results to show that logic ZOH scheme is not superior to ZOH scheme. A smart signal choosing algorithm is proposed in Section 5 to determine whether to use the out-of-order packets to obtain the improved performance. Finally, Section 6 concludes the paper and discusses further research directions.

Notation: Throughout this paper, $\mathbb{N}$ stands for the set of positive integers. ${\mathbb{R}}^n$ denotes the n-dimensional Euclidean space. ${\mathbb{R}}^{m\times n}$ is the set of all m × n real matrices. For symmetric matrices P and Q, the notation P > Q (respectively, P ⩾ Q) means that matrix P − Q is positive definite (respectively, positive semi-definite). I_n is an identity matrix of n × n dimensions. diag(A₁, A₂, … , A_n) denotes the block-diagonal matrix. Ones(n, m) is an m-by-n matrix of ones.