Maximum Allowable Transmission Interval Research Articles

Tradeoffs between quality-of-control and quality-of-service in large-scale nonlinear networked control systems

In this paper we study input-to-state stability (ISS) of large-scale networked control systems (NCSs) in which sensors, controllers and actuators are connected via multiple (local) communication networks which operate asynchronously and independently of each other. We model the large-scale NCS as an interconnection of hybrid subsystems, and establish rather natural conditions which guarantee that all subsystems are ISS, and have an associated ISS Lyapunov function. An ISS Lyapunov function for the overall system is constructed based on the ISS Lyapunov functions of the subsystems and the interconnection gains. The control performance, or “quality-of-control”, of the overall system is then viewed in terms of the convergence rate and ISS gain of the associated ISS Lyapunov function. Additionally, the “quality-of-service” of the communication networks is viewed in terms of the maximum allowable transmission interval (MATI) and the maximum allowable delay (MAD) of the network, and we show that the allowable quality-of-service of the communication networks is constrained by the required ISS gains and convergence rate of the hybrid subsystem corresponding to that network. Our results show that the quality-of-control of the overall system can be improved (or degraded) by improving (or relaxing) the quality-of-service of the communication networks. Alternatively, when relaxing the quality-of-service of one communication network, we can retain the quality-of-control of the overall system by improving the quality-of-service of one or more of the other communication networks. Our general framework will formally show these intuitive and insightful tradeoffs.

Tradeoffs Between Transmission Intervals and Delays for Decentralized Networked Control Systems Based on a Gain Assignment Approach

This brief investigates the stability problem of interconnected networked control systems in which there are many local networks, and each network is independent of the others. Several transmission imperfections, including variable transmission intervals, variable transmission delays, and communication constraints, are permitted by each local network. A gain assignment criterion is proposed to assign the gain closely related to the maximum allowable transmission interval (MATI) and maximum allowable delay (MAD) of each local network. Moreover, the tradeoffs between the MATI and MAD of each local network can be computed by solving a series of differential equations with the acquired gains. Finally, a commonly used example is given to show the improvement of the obtained results over the existing literature.

Emulation-based stabilization of networked control systems implemented on FlexRay

We investigate the emulation controller design approach for nonlinear networked control systems (NCS) with FlexRay. FlexRay is a deterministic communication protocol which is increasingly used in the automotive industry as it provides a high bandwidth and allows for safety critical applications. It is characterized by pre-set communication cycles that are subdivided into static and dynamic segments; the data transmissions are scheduled by different rules depending on the segment. We propose for the first time a hybrid model of NCS with FlexRay for this purpose. We show, under reasonable assumptions, that the asymptotic stability property ensured by the controller in the absence of communication constraints is preserved when the latter is implemented over FlexRay with sufficiently frequent data transmission. In particular, we assume that on each communication segment, the data transmissions are governed by uniformly globally exponentially stable protocols. This covers the case when the round-robin protocol is implemented on the static segment and the try-once-discard protocol is implemented on the dynamic segment. We provide explicit maximum allowable transmission interval bounds that guarantee stability.

Protocol sequence and control co‐design for a collection of networked control systems

SummaryThis paper is concerned with the simultaneous stabilization of a collection of plants shared by the wireless network with capacity limitation. We use most regular binary sequences (MRBS) to control the medium access status of the plants. The design procedure of the scheduling policy translates to determine two parameters of the MRBS. With the MRBS protocol, each plant is essentially a sampled‐data control system with time varying sampling intervals. We derive a sufficient condition for determining the MRBS protocol that guarantees the controllability, observability, and stability of each plant. Most importantly, we give a methodology for MRBS protocol and controller co‐design, in which the controller has switching gains that are piecewise constant and dependent on the sampling intervals yielded by the MRBS. The main results are established using piecewise Lyapunov functional and the average dwell time technique. It is shown that the method can guarantee simultaneous stabilization of the collection of plants robustly in situations where the controller gain does not match the sampling interval or the sampling interval violates the maximum allowable transmission interval criteria. A numerical example is given to demonstrate the effectiveness of the co‐design method. Copyright © 2015 John Wiley & Sons, Ltd.

Stability Analysis of Networked Control Systems based on L p Properties

To handle the communication constraint imposed by the serial communication channel in networked control systems (NCSs), we discuss a popular dynamic scheduling protocol called Maximum-Error-First (MEF) protocol. An important parameter in this protocol is the maximum allowable transmission interval (MATI), which indicates the communication cost for the task of control. To take as large MATI as possible under the constraint of guaranteeing stability is one formalization of the design requirement to consume as little communication resources as possible with the control performances ensured. A method to estimate this parameter based on the ℒp norm is suggested in this paper, which gives larger estimation than some methods do in the literature through simulation examples.

Stability Analysis of Spatially Invariant Interconnected Systems with Networked Communication

In this paper tractable stability conditions are presented for a system consisting of an infinite number of spatially invariant subsystems interconnected through communication networks. The networks transmit packets asynchronously and independently of each other and are equipped with scheduling protocols that determine which actuator, sensor or controller node is allowed access to the network. The overall system is modeled as an interconnection of an infinite number of spatially invariant hybrid subsystems. Based on this framework, conditions leading to a maximally allowable transmission interval (MATI) for all of the individual communication networks is derived such that uniform global asymptotic stability (UGAS) of the overall system is guaranteed. These conditions only involve the local dynamics of a single hybrid subsystem in the interconnection. In the case of linear subsystems the conditions can be stated in terms of linear matrix inequalities thereby making them numerically tractable. An illustrative example of a platoon of vehicles is used to demonstrate the newly obtained results and their applications.

Tracking Control for Nonlinear Networked Control Systems

We investigate the tracking control of nonlinear networked control systems (NCS) affected by disturbances. We consider a general scenario in which the network is used to ensure the communication between the controller, the plant and the reference system generating the desired trajectory to be tracked. The communication constraints induce non-vanishing errors (in general) on the feedforward term and the output of the reference system, which affect the convergence of the tracking error. As a consequence, available results on the stabilization of equilibrium points for NCS are not applicable. Therefore, we develop an appropriate hybrid model and we give sufficient conditions on the closed-loop system, the communication protocol and an explicit bound on the maximum allowable transmission interval guaranteeing that the tracking error converges to the origin up to some errors due to both the external disturbances and the aforementioned non-vanishing network-induced errors. The results cover a large class of the so-called uniformly globally asymptotically stable protocols which include the well-known round-robin and try-once-discard protocols. We also introduce a new dynamic protocol suitable for tracking control. Finally, we show that our approach can be used to derive new results for the observer design problem for NCS. It has to be emphasized that the approach is also new for the particular case of sampled-data systems.

Stability Analysis of Nonlinear Switched Networked Control Systems with Periodical Packet Dropouts

The input-to-state stability problem of a class of nonlinear switched networked control systems subject to time-varying transmission intervals, periodical packet dropouts, and communication constraints is investigated. By adopting the extended input-to-state stability(eISS) protocol and constructing a novel Lyapunov function, the input-to-state stability properties of such systems are discussed. Then, by making use of the small-gain theorem, the maximum allowable transmission interval to guarantee system stability is obtained. A batch reactor is finally considered to demonstrate the effectiveness of the proposed method.

An improved self-triggered implementation for linear controllers

Research in networked control systems raised the importance of understanding what are the timing requirements for control. In recent years this problem has been attacked from multiple angles including the computation of Maximal Allowable Transmission Intervals, event-triggered, and self-triggered controller implementations. In a self-triggered implementation the controller is responsible for computing the next time instant at which the actuator values should be updated by evaluating the control law on fresh sensor measurements. One of the main challenges in self-triggered control is how to perform the exact calculation of the time at which these updates should take place. In this paper we present a new technique to compute lower bounds on the self-triggered update times in a computationally light manner. We evaluate the algorithm on numerical examples and we observe that the algorithm performs well when compared to other existing methods and provides tight lower bounds on the exact update times. Additionally, we propose a Semidefinite Programming-based technique that produces triggering conditions that are less conservative than the existing ones and for which the update times are larger.

Stability analysis of networked control systems: A sum of squares approach

This paper presents a sum of squares (SOS) approach to the stability analysis of networked control systems (NCSs) incorporating bounded time-varying delays, bounded time-varying transmission intervals and a shared communication medium. A shared communication medium imposes that per transmission only one node, which consists of several actuators or sensors, can access the network and transmit its corresponding data. Which node obtains access is determined by a network protocol. We will provide mathematical models that describe these NCSs and transform them into suitable hybrid systems formulations. Based on these hybrid systems formulations we construct Lyapunov functions using SOS techniques that can be solved using LMI-based computations. This leads to several beneficial features: (i) we can deal with plants and controllers which are described by nonlinear (piecewise) polynomial differential equations, (ii) we can allow for non-zero lower bounds on the delays and transmission intervals in contrast with various existing approaches, (iii) we allow more flexibility in the Lyapunov functions thereby obtaining less conservative estimates of the maximal allowable transmission intervals (MATI) and maximal allowable delay (MAD), and finally (iv) it provides an automated method to address stability analysis problems in NCS. Several numerical examples illustrate the strengths of our approach.

A Framework for the Observer Design for Networked Control Systems

This technical note proposes a framework for the observer design for networked control systems (NCS) affected by disturbances, via an emulation-like approach. The proposed model formulation allows us to consider various static and dynamic time-scheduling protocols, in-network processing implementations and encompasses sampled-data systems as a particular case. Provided that the continuous-time observer is robust to the measurement errors (in an appropriate sense) we derive bounds on the maximum allowable transmission interval that ensure the convergence of the observation errors under network-induced communication constraints. The stability analysis is trajectory-based and utilizes small-gain arguments. A number of observers can be combined and used within our approach to obtain estimators for NCS.

On emulated nonlinear reduced-order observers for networked control systems

We consider a general class of nonlinear reduced-order observers and show that the global asymptotic convergence of the observation error in the absence of network-induced constraints is maintained for the emulated observer semiglobally and practically (with respect to the maximum allowable transmission interval) when system measurements are sent through a communication channel. Networks governed by a Lyapunov uniformly globally asymptotically stable protocol are investigated. Our results can be used to synthesize various observers for networked control systems for a range of network configurations, as we illustrate it by considering classes of immersion and invariance observers which include the circle-criterion observers.

New delay-dependent stabilisation criterion for a class of networked control systems

Networked control systems (NCSs) have been one of the main research areas in academia as well as in industry for many decades. In this paper, the study investigates the problem of delay-dependent stability criterion based on a newly developed NCS model including all these network phenomena and the new Lyapunov functional candidate for a class of NCSs, which the plant and the controller are spatially separated and the control loop is closed through a communication network. By introducing new Lyapunov functional candidate and free-weighting matrices techniques, the bounds on the maximally allowable transmission interval (MATI) are derived, which guarantee stability of the NCS in the presence of communication constraints, and the criteria of delay-dependent asymptotical stability for systems are analysed. The efficacy and feasibility of the proposed methods is shown by presenting simulation results.

Observer design for classes of non-linear networked control systems

Assuming a class of continuous-time observers is known for a given non-linear system, an observation structure is derived when sensors information is subject to network-induced communication constraints. The approach is based on the recent results on hybrid observers for sampled-data systems by Karafyllis and Kravaris (2009). Considering two classes of protocols, some asymptotic stability properties are shown to hold for the observation error, under some conditions, and explicit bounds on the maximum allowable transmission interval are given.

High Gain Observer Design for Some Networked Control Systems

New results on high gain observer design for networked control systems via an emulation-like approach are presented. By using a general framework and a Lyapunov approach, we derive some explicit conditions on the maximum allowable transmission interval that ensure an exponential convergence of the observation error for a large class of network protocols.

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

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.

High gain observer design for some networked control systems

New results on emulation of a high gain observer over networks are presented. Using a general framework and a suitable Lyapunov function, some explicit conditions on the maximum allowable transmission interval are given for a large class of network protocols.

NETWORKED CONTROL SYSTEMS: AN EMULATION APPROACH TO CONTROLLER DESIGN

We overview our recent work on a design approach for networked control systems (NCS) that resembles controller emulation for sampled-data systems. In the first step, we design a controller ignoring the network and, in the second step, we implement the designed controller over the network with sufficiently fast transmissions and a given protocol. Our results have several features: (i) they apply to general nonlinear systems with disturbances; (ii) we obtain explicit (often non-conservative) bounds on the maximal allowable transmission interval that guarantee stability; (iii) and we show that this approach is valid for a wide range of network scheduling protocols. This provides a flexible framework for design of NCS that is amenable to various extensions and modifications, such as a treatment of dropouts and stochastic protocols, combined controller/protocol design for linear plants, and so on.