Necessary and Sufficient Stabilizing Conditions for Networked Control Systems With Simultaneous Transmission Delay and Packet Dropout

Tan, Cheng; Zhang, Huanshui

doi:10.1109/tac.2016.2614887

Cited by 63 publications

(44 citation statements)

References 16 publications

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“…Constraint C b ≤ 1 can be shown as follows, Recall that a matrix is totally unimodular if the determinant of its any square submatrix is 0, 1 or −1. Then let us take the following submatrixC with row indices (1,3,6,12,14,15,16) and column indices (1,2,3,7,8,10,12), i.e., It turns out that the determinate ofC is −2. Thus C is not totally unimodular.…”

Section: B An Example To Show That the Constraint Matrix Of The Vectmentioning

confidence: 99%

“…In addition, throughput, which is termed timely throughput in the delay-constrained scenario [13], [14], [15], [8], is also important to such applications. Taking NCSs as an example, the control system can be stabilized if the control messages arrive before the predetermined deadlines and the dropout rate is below a threshold (which equivalently means that the timely throughput is above a threshold) [16], [17]. Taking tactile Internet as another example, the timely throughput is a measure of reliability [10].…”

Section: Introductionmentioning

confidence: 99%

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Delay-Constrained Input-Queued Switch

Deng

Wong

Chen

et al. 2018

IEEE J. Select. Areas Commun.

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In this paper, we study the delay-constrained inputqueued switch where each packet has a deadline and it will expire if it is not delivered before its deadline. Such new scenario is motivated by the proliferation of real-time applications in multimedia communication systems, tactile Internet, networked controlled systems, and cyber-physical systems. The delay-constrained input-queued switch is completely different from the well-understood delay-unconstrained one and thus poses new challenges. We focus on three fundamental problems centering around the performance metric of timely throughput: (i) how to characterize the capacity region? (ii) how to design a feasibility/throughput-optimal scheduling policy? and (iii) how to design a network-utility-maximization scheduling policy? We use three different approaches to solve these three fundamental problems. The first approach is based on Markov Decision Process (MDP) theory, which can solve all three problems. However, it suffers from the curse of dimensionality. The second approach breaks the curse of dimensionality by exploiting the combinatorial features of the problem. It gives a new capacity region characterization with only a polynomial number of linear constraints. The third approach is based on the framework of Lyapunov optimization, where we design a polynomial-time maximum-weight T-disjoint-matching scheduling policy which is proved to be feasibility/throughput-optimal. Our three approaches apply to the frame-synchronized traffic pattern but our MDP-based approach can be extended to more general traffic patterns.

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Section: B An Example To Show That the Constraint Matrix Of The Vectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Delay-Constrained Input-Queued Switch

Deng

Wong

Chen

et al. 2018

IEEE J. Select. Areas Commun.

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“…where > 0 is a sufficiently small positive real number into (14) and then we obtain a set of {x t (s, a)}, which is further inserted to (15) to construct the i.i.d. scheduling policy.…”

Section: Stability Condition Of Our Wncsmentioning

confidence: 99%

On Stability Condition of Wireless Networked Control Systems under Joint Design of Control Policy and Network Scheduling Policy

Deng

Tan

Wong

2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper, we study a wireless networked control system (WNCS) with N ≥ 2 sub-systems sharing a common wireless channel. Each sub-system consists of a plant and a controller and the control message must be delivered from the controller to the plant through the shared wireless channel. The wireless channel is unreliable due to interference and fading. As a result, a packet can be successfully delivered in a slot with a certain probability. A network scheduling policy determines how to transmit those control messages generated by such N subsystems and directly influences the transmission delay of control messages. We first consider the case that all sub-systems have the same sampling period. We characterize the stability condition of such a WNCS under the joint design of the control policy and the network scheduling policy by means of 2 N linear inequalities. We further simplify the stability condition into only one linear inequality for two special cases: the perfect-channel case where the wireless channel can successfully deliver a control message with certainty in each slot, and the symmetric-structure case where all sub-systems have identical system parameters. We then consider the case that different sub-systems can have different sampling periods, where we characterize a sufficient condition for stability.

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“…In fact, as said in [14]- [15], the problems that packet dropout and delay occur simultaneously are more difficult and remain challenging. However, recently, some researches have concentrated on the NCSs simultaneously involved both packet losses and delay, such as [16] and [17]. More concretely, under the assumption that packet loss and time-delay may occur simultaneously in NCSs, [16] obtained the necessary and sufficient stabilizing conditions based on the algebraic Riccati equation or Lyapunov equation.…”

mentioning

confidence: 99%

“…However, recently, some researches have concentrated on the NCSs simultaneously involved both packet losses and delay, such as [16] and [17]. More concretely, under the assumption that packet loss and time-delay may occur simultaneously in NCSs, [16] obtained the necessary and sufficient stabilizing conditions based on the algebraic Riccati equation or Lyapunov equation. As to the NCSs with measurement packet dropout and delay, [17] expressed the optimal controller with feedback gain based on a standard difference Riccati equation and an equivalent condition of stabilizing in mean square sense was given.…”

mentioning

confidence: 99%

Optimal Control and Stabilization for Networked Systems With Input Delay and Markovian Packet Losses

Han

Zhang

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

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The mean square stabilization problem for discretetime networked control systems (NCSs) is investigated in this article. What the difference from most previous works is that input delay and packet losses occur simultaneously in the communication channel, moreover, the data packet dropout is modeled as a time-homogeneous Markov process which will bring some difficulties in solving the problem due to the temporal correlation. The contributions in this paper can be summarized as two points. Firstly, the equivalence condition for the solvability of linear quadratic optimal problem in finite horizon subject to the discrete-time NCSs is expressed by solving the forward and backward stochastic difference equations (FBSDEs-M) which is derived from the maximum principle involving Markov jump and delay. Secondly, under basic assumption, the necessary and sufficient condition of mean square stabilization is given by the solutions to the coupled algebraic Riccati equations with Markov jump (CAREs-M). To our best knowledge, the problems studied in this paper are new because most previous works mainly discussed the case of only delay or packet dropout in NCSs.

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Necessary and Sufficient Stabilizing Conditions for Networked Control Systems With Simultaneous Transmission Delay and Packet Dropout

Cited by 63 publications

References 16 publications

Delay-Constrained Input-Queued Switch

Delay-Constrained Input-Queued Switch

On Stability Condition of Wireless Networked Control Systems under Joint Design of Control Policy and Network Scheduling Policy

Optimal Control and Stabilization for Networked Systems With Input Delay and Markovian Packet Losses

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