Networked control systems (NCSs) have, in recent years, brought many innovative impacts to control systems. However, great challenges are also met due to the network-induced imperfections. Such network-induced imperfections are handled as various constraints, which should appropriately be considered in the analysis and design of NCSs. In this paper, the main methodologies suggested in the literature to cope with typical network-induced constraints, namely time delays, packet losses and disorder, time-varying transmission intervals, competition of multiple nodes accessing networks, and data quantization are surveyed; the constraints suggested in the literature on the first two types of constraints are updated in different categorizing ways; and those on the latter three types of constraints are extended.

Network-Induced Constraints in Networked Control Systems—A Survey

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.

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Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

Networked control systems (NCSs) are systems whose control loops are closed through communication networks such that both control signals and feedback signals can be exchanged among system components (sensors, controllers, actuators, and so on). NCSs have a broad range of applications in areas such as industrial control and signal processing. This survey provides an overview on the theoretical development of NCSs. In-depth analysis and discussion is made on sampled-data control, networked control, and event-triggered control. More specifically, existing research methods on NCSs are summarized. Furthermore, as an active research topic, network-based filtering is reviewed briefly. Finally, some challenging problems are presented to direct the future research.

Survey on Recent Advances in Networked Control Systems

This paper combines two important control techniques for reducing communication traffic in control networks, namely, model-based networked control systems (MB-NCS) and event-triggered control. The resulting framework is used for stabilization of uncertain dynamical systems and is extended to systems subject to quantization and time-varying network delays. The use of a model of the plant in the controller node not only generalizes the zero-order-hold (ZOH) implementation in traditional event-triggered control schemes but it also provides stability thresholds that are robust to model uncertainties. The effects of quantized measurements are especially important in the selection of stabilizing thresholds. We are able to design error events based on the quantized variables that yield asymptotic stability compared to similar results in event-triggered control that consider nonquantized measurements which, in general, are not possible to use in digital computations. With respect to MB-NCS, the stability conditions presented here do not need explicit knowledge of the plant parameters as in previous work but are given only in terms of the parameters of the nominal model and some bounds in the model uncertainties. We consider the joint adverse effects of quantization and time delays and emphasize the expected tradeoff between the selection of quantization parameters and the admissible network induced delays.

https://www3.nd.edu/~pantsakl/Publications/445-TAC.pdf

Model-Based Event-Triggered Control for Systems With Quantization and Time-Varying Network Delays

In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. Communication constraints impose that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is orchestrated by a network protocol, such as, the Round-Robin (RR) and the Try-Once-Discard (TOD) protocol. In this paper, we generalize the mentioned protocols to novel classes of so-called “periodic” and “quadratic” protocols. By focusing on linear plants and controllers, we present a modeling framework for NCSs based on discrete-time switched linear uncertain systems. This framework allows the controller to be given in discrete time as well as in continuous time. To analyze stability of such systems for a range of possible transmission intervals and delays, with a possible nonzero lower bound, we propose a new procedure to obtain a convex overapproximation in the form of a polytopic system with norm-bounded additive uncertainty. We show that this approximation can be made arbitrarily tight in an appropriate sense. Based on this overapproximation, we derive stability results in terms of linear matrix inequalities (LMIs). We illustrate our stability analysis on the benchmark example of a batch reactor and show how this leads to tradeoffs between different protocols, allowable ranges of transmission intervals and delays. In addition, we show that the exploitation of the linearity of the system and controller leads to a significant reduction in conservatism with respect to existing approaches in the literature.

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Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach

We consider continuous time switched systems that are stabilized via a computer. Several factors (sampling, computer computation, communications through a network, etc.) introduce model uncertainties produced by unknown varying feedback delays. These uncertainties can lead to instability when they are not taken into account. Our goal is to construct a switched digital control for continuous time switched systems that is robust to the varying feedback delay problem. The main contribution of this note is to show that the control synthesis problem in the context of unknown time varying delays can be expressed as a problem of stabilizability for uncertain systems with polytopic uncertainties

Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays

Equivalence between the Lyapunov-Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems

This paper is dedicated to the modelling of LTI continuous time systems in digital control loops We consider the digital control problem on non-uniform sampling periods Moreover, we assume that time varying delays that may have a variation range larger than a sampling period affect the closed-loop Our goal is to present a unique model that is able to include these problems simultaneously and that can be handled by classical control synthesis tools We present a new event based discrete-time model (an exponential uncertain system with delay) and we show that the stabilizability of this system can be achieved by finding a control for a switched polytopic system with an additive norm bounded uncertainty The methodology is extended to the case of switched system

Analysis and control of LTI and switched systems in digital loops via an event-based modelling

The problem of robust and guaranteed stabilization is addressed for switched affine systems using sampled state feedback controllers. Based on the existence of a control Lyapunov function for a relaxed system, we propose three sampled-data controls. Global attracting sets, computed by solving a sequence of optimization problems, guarantee practical and global asymptotic stabilization for the whole system trajectories. In addition, robust margins with respect to parameters uncertainties and non uniform sampling are provided using input-to-state stability. Finally, a buck-boost converter is considered to illustrate the effectiveness of the proposed approaches.

/pdf/switched-affine-systems-using-sampled-data-controllers-2upysqzlre.pdf

Claude Iung

Papers

Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays

Equivalence between the Lyapunov-Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems

Analysis and control of LTI and switched systems in digital loops via an event-based modelling

Switched Affine Systems Using Sampled-Data Controllers: Robust and Guaranteed Stabilization

Bumpless transfer for switched linear systems