Architectures and coder design for networked control systems

In networked control systems (NCSs) achievable performance is limited by the communication links employed to transmit signals in the loop. In the present work, we characterise LTI coding systems which optimise performance for various NCS architectures. We study NCSs where the communication link is situated between plant output and controller, and NCSs where the communication link is located between controller and actuator. Furthermore, we present a novel NCS architecture, which is based upon the Youla parameterisation. We show that, which of these architectures gives best performance depends, inter alia, upon characteristics of a related non-networked design, plant disturbances and reference signal. A key aspect of our work, resides in the utilisation of fixed signal-to-noise ratio channel models which give rise to parsimonious designs, where channel utilisation is kept low. The results are verified with simulations utilising bit-rate limited channels.     

On Stability in the Presence of Analog Erasure Channel Between the Controller and the Actuator

Consider a discrete-time networked control system, in which the controller has direct access to noisy measurements of the output of the plant. However, information flows from the controller to the actuator via a channel that features Bernoulli erasure events. If an erasure occurs, the channel outputs an erasure symbol; otherwise, it transmits a real finite-dimensional vector. We determine necessary and sufficient conditions for the stabilizability of an unstable linear time-invariant finite-dimensional plant. Given a minimal state-space representation for the plant, the necessary and sufficient conditions for stabilizability are expressed in terms of the probability of erasure at the channel and of the spectral radius of the one-step state transition matrix. There are two main results in the technical note. The first result shows that if the actuator has processing capabilities, then the necessary and sufficient conditions for stabilizability remain unchanged with or without acknowledgements from the actuator to the controller. The second result shows that the stabilizability conditions are identical for two types of actuators: (Type I) Processing at the actuator has access to the plant's model;      

Feedback stabilization of uncertain systems in the presence of a direct link

We study the stabilizability of uncertain stochastic systems in the presence of finite capacity feedback. Motivated by the structure of communication networks, we consider a variable rate digital link. Such link is used to transmit state measurements between the plant and the controller. We derive necessary and sufficient conditions for internal and external stabilizability of the feedback loop. In accordance with previous publications, stabilizability of unstable plants is possible if and only if the link's average transmission rate is above a positive critical value. In addition, stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We also show that robustness can be increased at the expense of a higher transmission rate.     

Improving control performance across AWGN channels using a relay node†

Consider an unstable linear time-invariant system in which the sensor transmits information to a controller across an additive white Gaussian noise channel. The designer can optionally utilise a relay node to assist the controller; however, the total transmission power consumed by the sensor and the relay node is constant. We consider two topologies: (1) a Gaussian relay channel and (2) a cascade of two Gaussian point-to-point channels. We propose coding schemes and present sufficient conditions for the stabilisability of the plant through such schemes. The analysis suggests that it is useful to utilise a relay node, even if the total transmission power remains the same.     

Dynamic stabilization of regular linear systems

We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain. For this class of systems, we investigate the concepts of stabilizability and detectability, in particular, their invariance under feedback and their relationship to exponential stability. We introduce two concepts of dynamic stabilization, the first formulated as usual, with the plant and the controller connected in feedback, and the second with two feedback loops. Even for finite-dimensional systems, the second concept, stabilization with an internal loop in the controller, is more general. We argue that the more general concept is the natural one, and we derive sufficient conditions under which an observer-based stabilizing controller with an internal loop can be constructed     

Control over noisy channels

Communication is an important component of distributed and networked controls systems. In our companion paper, we presented a framework for studying control problems with a digital noiseless communication channel connecting the sensor to the controller. Here, we generalize that framework by applying traditional information theoretic tools of source coding and channel coding to the problem. We present a general necessary condition for observability and stabilizability for a large class of communication channels. Then, we study sufficiency conditions for Internet-like channels that suffer erasures.     

Control of Continuous-Time Linear Gaussian Systems Over Additive Gaussian Wireless Fading Channels: A Separation Principle

This note is concerned with the control of continuous-time linear Gaussian systems over additive white noise wireless fading channels subject to capacity constraints. Necessary and sufficient conditions are derived, for bounded asymptotic and asymptotic observability and stabilizability in the mean square sense, for controlling such systems. For the case of a noiseless time-invariant system controlled over a continuous-time additive white Gaussian noise channel, the sufficient condition for stabilizability and observability states that the capacity of the channel C must satisfy C > Sigma_{{i;Re(lambdai(A))ges0}} Re(lambda_i(A)), where A is the system matrix and lambda_i(A) denotes the eigenvalues of A. The necessary condition states that the channel capacity must satisfy C ges Sigma _{{i;Re(lambdai(A))ges0}} Re(lambda_i(A)). Further, it is shown that a separation principle holds between the design of the communication and the control subsystems, implying that the controller that would be optimal in the absence of the communication channel is also optimal for the problem of controlling the system over the communication channel.     

LQG optimality and separation principle for general discrete time partially observed stochastic systems over finite capacity communication channels

This paper is concerned with control of stochastic systems subject to finite communication channel capacity. Necessary conditions for reconstruction and stability of system outputs are derived using the Information Transmission theorem and the Shannon lower bound. These conditions are expressed in terms of the Shannon entropy rate and the distortion measure employed to describe reconstruction and stability. The methodology is general, and hence it is applicable to a variety of systems. The results are applied to linear partially observed stochastic Gaussian controlled systems, when the channel is an Additive White Gaussian Noise (AWGN) channel. For such systems and channels, sufficient conditions are also derived by first showing that the Shannon lower bound is exactly equal to the rate distortion function, and then designing the encoder, decoder and controller which achieve the capacity of the channel. The conditions imposed are the standard detectability and stabilizability of Linear Quadratic Gaussian (LQG) theory, while a separation principle is shown between the design of the control and communication systems, without assuming knowledge of the control sequence at the encoder/decoder.     

Relations between the stabilization properties of two classes of hereditary linear systems with commensurate delays

Two classes of hereditary linear systems each subjected to two alternative controller structures (one of a free delay dynamic nature while the other one includes delays under integral forms) are analysed from a stabilizability viewpoint. The first class of plants has pure commensurate delays in both state and input while the second has its time delayed contributions to the dynamics under integral form in the differential equations. Under certain weak conditions, the four closed-loop systems resulting from combining each open-loop plant structure with each controller structure can lead to identical state/output trajectories for appropriately related controller parametrizations. This allows the derivation of stabilizability results for any of the four closed-loop combinations of open-loop system plus controller by using results from the literature, each one being originally applicable to just one of the above combinations     

套代数框架下网络控制系统的鲁棒稳定性分析

研究级联双端口网络控制系统在被控对象、控制器和双端口通信信道中同时存在扰动的稳定性问题.当网络控制系统通过一系列双向通信信道进行信号传输时,系统建模为通过级联双端口网络进行连接.由于通信过程中会发生信息的失真和干扰,考虑双端口信道传输矩阵中的H_∞范数有界扰动以及被控对象和控制器中的gap型扰动,得到基于通信信道扰动服从范数有界时闭环系统与网络控制系统鲁棒稳定之间的关系,同时也以几何不等式的方式给出判定网络控制系统鲁棒稳定性的充分条件.数值算例表明结论是有效的.     

Remote Control Over Noisy Communication Channels: A First-Order Example

In this note, we consider a set up in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a noisy discrete channel. Our goal is to design codeword lengths of block source and channel encoders, and a controller to meet a model matching performance objective. Such design problems are difficult in general, as there is a strong interplay between control objectives and communication constraints, which forces the synthesis of controllers and encoder-decoder pairs to be done simultaneously. Current approaches typically fix one, while the other is designed to meet some objective. We first construct a model matching performance metric that captures the tradeoffs between coding the reference command to achieve more accuracy at the remote site and designing a controller to meet performance. We then simultaneously synthesize the controller and encoder codeword lengths that meet the specified objective for a first-order plant and model case. Finally, we illustrate performance sensitivity to the poles of the plant and model, and to the channel noise     

Optimal Signaling Policies for Decentralized Multicontroller Stabilizability Over Communication Channels

In this note, we study the problem of distributed control over communication channels, where a number of distributed stations collaborate to stabilize a linear system. We quantify the rate requirements and obtain optimal signaling, coding and control schemes for decentralized stabilizability in such multicontroller systems. We show that in the absence of a centralized decoder at the plant, there is in general a rate loss in decentralized systems as compared to a centralized system. This result is in contrast with the absence of rate loss in the stabilization of multisensor systems. Furthermore, there is rate loss even if explicit channels are available between the stations. We obtain the minimum data rates needed in terms of the open-loop system matrix and the connectivity graph of the decentralized system, and obtain the optimal signaling policies. We also present constructions leading to stability. In addition, we show that if there are dedicated channels connecting the controllers, rate requirements become more lenient, and as a result strong connectivity is not required for decentralized stabilizability. We determine the minimum number of such external channels leading to a stable system, in case strong connectivity is absent.     

一类线性不确定时滞混杂系统的稳定性

研究了一类具有不确定的线性参数及时滞的混杂系统，利用线性矩阵不等式策略和Riccati方法，给出了系统鲁棒稳定性和可稳定性的充分条件，并运用混杂状态反馈控制策略设计了控制器切换方案．最后的仿真实例表明了控制策略的有效性．     

INTEGRATED COMMUNICATION AND CONTROL SYSTEMS WITH OCCASIONAL INFORMATION FEEDBACK

Stabilizability is herein studied for linear discrete-time systems with occasional information feedback supplied by a remote controller via a communication channel with limited data-rate. A new concept called set-stabilizability is introduced, and sufficient and necessary stabilizability conditions on the quantization level and control precision are derived. Most importantly, a specific relationship between stabilizability and the communication data rate is established. For different network-induced delays that are assumed to be constant, time varying, and random, respectively, the lowest data rates sufficient/necessary for the system to be finite time set-stabilizable, Lyapunov stabilizable, and probability-1 stabilizable are obtained accordingly.     

Quadratic stabilization of linear networked control systems via simultaneous protocol and controller design

We derive conditions for quadratic stabilizability of linear networked control systems by dynamic output feedback and communication protocols. These conditions are used to develop a simultaneous design of controllers and protocols in terms of matrix inequalities. The obtained protocols do not require knowledge of controller and plant states but only of the discrepancies between current and the most recently transmitted values of nodes’ signals, and are implementable on controller area networks. We demonstrate on a batch reactor example that our design guarantees quadratic stability with a significantly smaller network throughput than previously available designs.     

Streaming video over variable bit-rate wireless channels

We consider streaming of video sequences over both constant and variable bit-rate (VBR) channels. Our goal is to enable decoding of each video unit before exceeding its displaying deadline and, hence, to guarantee successful sequence presentation even if the media rate does not match the channel rate. In this work, we show that the separation between a delay jitter buffer and a decoder buffer is in general suboptimal for VBR video transmitted over VBR channels. We specify the minimum initial delay and the minimum required buffer for a given video stream and a deterministic VBR channel. In addition, we provide some probabilistic statements in case that we observe a random behavior of the channel bit rate. A specific example tailored to wireless video streaming is discussed in greater detail and bounds are derived which allow guaranteeing a certain quality-of-service even for random VBR channels in a wireless environment. Simulation results validate the findings.     

Remote control of LTI systems over networks with state quantization

We consider a remote control system, where the plant and the controller are connected by a network cable, and study the problem of designing quantizers for its stabilization. It is assumed that the computation available on the plant side in the sensor/actuator is limited and also that broadcast of messages is allowed over the channel.     

Justification of input-output methods for systems with unboundedcontrol and observation

The authors present definitions of feedback stabilizability and detectability that are weaker than those previously appearing in the literature. Stabilizability and detectability (in this sense) are sufficient to ensure an equivalence between internal and external stability for well-posed systems. Furthermore, stabilizability and detectability are shown to be preserved under feedback (and other) connections. These results are linked to present a justification of input-output controller design methods for systems with unbounded control and observation     

Event-triggered transmission for linear control over communication channels

We consider an exponentially stable closed loop interconnection between a continuous-time linear plant and a continuous-time linear controller, and we study the problem of interconnecting the plant output to the controller input through a digital channel. We propose an event-triggered transmission policy whose goal is to transmit the measured plant output information as little as possible while preserving closed-loop stability. Global asymptotic stability is guaranteed when the plant state is available or when an estimate of the state is available (provided by a classical continuous-time linear observer). Under further assumptions, the transmission policy guarantees global exponential stability of the origin.     

有损信道下网络化系统的均方最优渐近跟踪

对于通讯信道具有丢包的网络化反馈控制系统, 运用乘性噪声模型来描述丢包这一信道不确定性, 并根据 网络化系统的结构特点提出了一种渐近跟踪控制器结构, 研究了该结构下系统的均方可镇定性以及均方最优渐近 跟踪与均方可镇定性的等价关系. 在此基础上, 运用随机均方最优控制理论给出了该系统均方最优渐近跟踪设计方 法, 该方法取决于广义代数黎卡提方程(MARE)的均方镇定解. 进一步, 本文提出了求解上述均方镇定解的新算法. 最后的仿真验证了对于信道具有丢包的网络化反馈系统最优渐近跟踪问题, 本文所提方法的有效性和可行性.