Sampling and control strategy: networked control systems subject to packet disordering

Abstract

This study proposes a novel sampling and control strategy to find a suboptimal sampling period sequence and control input sequence, such that a quadratic cost function of state and control input of a networked control system (NCS) with packet disordering is minimised. First, a discrete-time system model of the NCS with packet disordering, transmission delay and packet loss in terms of displacement values of packets is put forward. Second, a linear quadratic regulation (LQR) problem of the NCS is formulated, showing that the optimal controller depends on sampling period and quality of services (QoS) of networks. Interactive effects between sampling period and QoS of networks pose a challenge in solving the LQR problem of the NCS. To overcome this difficulty, different from traditional transmission-delay-based or packet-loss-based sampling scheme, a novel packet-disordering-based sampling period selection scheme is proposed. Furthermore, an algorithm is presented to find a suboptimal solution to the LQR problem in this study. Finally, simulation results demonstrate the effectiveness of the proposed approach. IntroductionFacing the increasing demand of control networks in industrial processes, commercial systems and traffic systems, a rapidly increasing focus on networked control systems (NCSs) has been witnessed [1][2][3]. NCSs have been hotspots of research in the past decades. The introduction of control networks can improve the efficiency, flexibility and reliability of these applications, reducing installation, maintenance, reconfiguration and costs. However, some unexpected phenomena potentially occur in network channels including transmission delay, packet loss and packet disordering and so on [4,5]. Therefore, different from traditional control systems, optimal control problems of NCSs require not only control system design, but also network system design. In this paper, we investigate the effects of sampling rate and packet disordering on solution of linear quadratic regulation (LQR) problem. We first formulate the LQR problem for the following continuous linear systemẋwhere x ∈ R n and u ∈ R m , respectively, are state and control input of the plant, and A ∈ R n×n and B ∈ R n×m are matrices with appropriate dimensions. The term t 0 is the initial time instant and x 0 is the initial state. Consider the following quadratic performance index for system (1)where Q ∈ R n×n and R ∈ R m×m are positive semi-definite matrix and positive definite matrix, respectively, and the term t f is the terminal time instant.The control input is assumed to be piecewise constantwhere u k = u(t k ), t k is the kth sampling time instant with 0 ≤ t 0 < t 1 < · · · < t k < · · · ≤ t f , and h k = t k+1 − t k is called sampling period. We assume h min ≤ h k ≤ h max , where h max and h min are the maximum and minimum values of the sampling period, respectively. For given sampling periods, the optimal control input u k that minimises the cost function (2) for system (1) can be analytically determined through solving the disc...

Sliding mode control for non‐linear networked control systems subject to packet disordering via prediction method

“… represents , namely, , which signifies the control input signal and also signifies the system of NCS (13). Here, we decide the subsystem switched is subject to the Markovian jumping process [8, 26]. Moreover, , , , .…”

“…Li et al . [8] established a novel sampling control strategy in the NCS subject to packet disordering. Xie et al .…”

Network‐based integral sliding mode control for descriptor systems with event‐triggered sampling scheme

“…Networked control systems (NCSs) are a category of systems consist of controllers, sensors, and actuators; and are connected over a common network medium . Different from traditional control systems, NCSs have great advantages like simple installation and low cost . In recent years, many outstanding results have been published.…”

“…12,13 Different from traditional control systems, NCSs have great advantages like simple installation and low cost. 14,15 In recent years, many outstanding results have been published. However, most results are time-triggered scheme (TTS).…”

Networked filtering with Markov transmission delays and packet disordering

“…It should be pointed out that if the packet disordering happens, the data packets to be transmitted are not necessary to follow the principle of ‘first send–first arrive’ as assumed in most existing works [21]. Control problems for networked systems with packet disordering have been extensively investigated (see [22–24], and the references therein), while the packet disordering issues are also intensively studied in the field of state estimation [25, 26]. Particularly, the filter design problem has been studied in [25] for networked systems with the phenomenon of Markov delays and packet losses.…”